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Tag Circle -- Asymptote Gallery

đź”—animations-fig002

Show animations/fig0020.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Animation
Tags : #Animation | #Geometry | #Circle

import geometry;
import animate;
settings.tex = "pdflatex";

animation A;
size(12cm);

for (int a = 1; a < 20; ++a) {
  save();
  point P = (-4.5, 0); dot(P);
  inversion inv = inversion(1, P);
  line l1 = line((0, 0), (-0.35, 1)), l2 = line((0, 0), (0.35, 1));
  path g1 = inv*l1, g2=inv*l2;

  fill(g1^^g2, evenodd+lightgrey); draw(g1, linewidth(bp));
  draw(g2, linewidth(bp));

  for (int i:new int[]{-1, 1}) {
    point P = (0, 3i/a);
    triangle t = triangle(shift(P)*hline, l1, l2);
    int n = a;

    for (int j = 0; j <= n; ++j) {
      circle C = excircle(t.AB);
      t = triangle(shift(angpoint(C, i*90))*hline, l1, l2);
      circle Cp = inv*C;
      path g = Cp;

      fill(g, 0.95*yellow);
      draw(g, bp+red); draw(g, blue);
    }
  }

  picture pic;
  add(pic, bbox(5mm, Fill(rgb(0.95, 0.95, 0.8))));
  A.add(pic);
  restore();
}

A.pdf(keep = true);

đź”—animations-fig004

Show animations/fig0040.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Animation
Tags : #Geometry | #Animation | #Triangle | #Circle | #Locus

import geometry;
import animate;
animation Anim;

size(12cm);

circle C=circle(origin, 1);
draw(C);
point A=point(C, 0), B, M;
guide locus;

for (real a=0.001; a < 360; a += 5) {
  save();
  B=angpoint(C,a);
  triangle t=triangle(origin, A, B);
  draw(t);
  draw(incircle(t), bp+0.8*blue);
  triangle intouch=intouch(t);
  draw(intouch, dot);
  M=intouch(t.AC);
  label("$N$", Label("$M$", 0.8*red), "$P$", intouch);
  dot(M, 0.8*red);
  locus=locus..M;
  draw(locus, bp+0.8*red);
  Anim.add();
  restore();
}

Anim.movie();

đź”—generalities-fig011

Figure generalities 011 Generated with Asymptote

Show generalities/fig0110.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Circle | #Fixedscaling | #Size

size(10cm,0);

draw(scale(4)*unitcircle);
dot((0, 0));
dot((4, 0));

fixedscaling((-8, -8),(6, 6));
shipout(bbox(Fill(lightgrey)));

đź”—generalities-fig056

Figure generalities 056 Generated with Asymptote

Show generalities/fig0560.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Fill/Unfill | #Shading | #Circle

size(8cm,0);

pair A=(0.35,0.35), B=(0.6,0.6);

radialshade(unitsquare,black,A,0.15,lightgrey,B,.6);

dot(A,.8red);
dot(B,blue+grey);
draw(shift(A)*scale(.15)*unitcircle,dashed+.8red);
draw(shift(B)*scale(.6)*unitcircle,dashed+blue+grey);
clip(unitsquare);

đź”—generalities-fig062

Figure generalities 062 Generated with Asymptote

Show generalities/fig0620.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Opacity | #Fill/Unfill | #Circle | #Transform/scale/shift/rotate

size(10cm, 0);

path cle=unitcircle;

draw((-1.5, 0)--(2.5, 0), linewidth(10mm));
filldraw(cle, red+opacity(.5));
filldraw(shift((1, 0))*cle, blue+opacity(.5));

shipout(format="pdf");

đź”—generalities-fig092

Figure generalities 092 Generated with Asymptote

Show generalities/fig0920.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Circle

size(6cm,0);

draw(E--N--W--S--cycle,.5red+1mm);

draw(E..N..W..S..cycle);
dot(E..N..W..S..cycle,red);

đź”—generalities-fig093

Figure generalities 093 Generated with Asymptote

Show generalities/fig0930.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Size | #Path | #Circle

size(0,0);
pair O=0;

draw(circle(O,4cm));
dot(circle(O,4cm), red+4bp);

đź”—generalities-fig094

Figure generalities 094 Generated with Asymptote

Show generalities/fig0940.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Size | #Path | #Circle

size(6cm);

draw(unitcircle, dot);
dotfactor*=3;
draw(shift(-0.5,-0.5)*unitsquare, dot(blue,Fill(red)));

đź”—generalities-fig097

Figure generalities 097 Generated with Asymptote

Show generalities/fig0970.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Size | #Path | #Circle

size(6cm,0);

//Return Circle AB diameter
path circle(pair A, pair B)
{
  return shift(midpoint(A--B))*scale(abs(A-B)/2)*unitcircle;
}

pair A=(0,0), B=(1,0);

draw(circle(A,B));
dot(A--B);

đź”—generalities-fig098

Figure generalities 098 Generated with Asymptote

Show generalities/fig0980.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Size | #Path | #Circle

size(6cm,0);

//Return Circle AB diameter
path circle(pair A, pair B)
{
  return shift(midpoint(A--B))*scale(abs(A-B)/2)*unitcircle;
}

pair A=(0,0), B=(3,0), C=(2,1);

draw(A--B,.8blue);
draw(A--C,.8red);
draw(B--C,.8green);
draw(circle(A,B),.8blue);
draw(circle(A,C),.8red);
draw(circle(B,C),.8green);

đź”—generalities-fig099

Figure generalities 099 Generated with Asymptote

Show generalities/fig0990.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Size | #Path | #Circle | #Function creation

size(6cm,0);

//Return Circle AB diameter
path circle(pair A, pair B)
{
  return shift(midpoint(A--B))*scale(abs(A-B)/2)*unitcircle;
}

pair A=(0,0), B=(1,0), C=(2,0);
path cleAB=circle(A,B);
path cleAC=circle(A,C);

for(real t=0; t<length(cleAB); t+=0.01)
  fill(circle(point(cleAB,t),point(cleAC,t)));

đź”—generalities-fig100

Figure generalities 100 Generated with Asymptote

Show generalities/fig1000.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Circle | #Arc

size(0,0);
pair O=0;

defaultpen(linewidth(2mm));
draw(arc(O,4cm,0,60), .8red, BeginPenMargin);
draw(arc(O,4cm,60,120), .7green, PenMargins);
draw(arc(O,-4cm,0,120), .7blue);

đź”—generalities-fig101

Figure generalities 101 Generated with Asymptote

Show generalities/fig1010.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Circle | #Picture | #Transform/scale/shift/rotate | #Array

size(8cm,0);

picture pic;
pen [] P={.8red,.7green,blue+.5grey,yellow+.6grey};

fill(scale(10)*unitcircle,.2blue);

for (int i = 0; i <= 3; ++i)
  draw(pic, arc((0,0),10,i*90,(i+1)*90), P[i]);

for (real i = 1; i <= 10; i+=.05)
  add(rotate(90*i)*scale(1/i)*pic);

đź”—generalities-fig123

Figure generalities 123 Generated with Asymptote

Show generalities/fig1240.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Circle

size(8cm);
draw(unitcircle, linewidth(bp));
pen p;
for (int t=-88; t <= 88; t += 2) {
  if(t%5 == 0) {
    p=linewidth(bp);
    draw((0,1){dir (t-90)}..{dir (270-t)}(0,-1), linewidth(bp));
  } else p=currentpen;
  draw((Cos(t),Sin(t)){dir(180+t)}..{dir(180-t)}(-Cos(t),Sin(t)), p);
}

đź”—generalities-fig134

Figure generalities 134 Generated with Asymptote

Show generalities/fig1350.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Circle

size(0,0);

path pt1=scale(4cm)*unitcircle;
path pt2=scale(2cm)*unitcircle;

draw(pt1^^pt2);
dot(pt1^^pt2);

đź”—generalities-fig135

Figure generalities 135 Generated with Asymptote

Show generalities/fig1360.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Circle | #Point/Dot | #Transform/scale/shift/rotate

size(0,0);

path cle=scale(4cm)*unitcircle;

draw(cle);

for(real i=0; i<=length(cle); i+=.2)
  {
    dot(point(cle,i));
    draw((0,0)--point(cle,i),dotted);
  }

đź”—generalities-fig136

Figure generalities 136 Generated with Asymptote

Show generalities/fig1370.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Circle | #Loop/for/while

size(0,0);

path cle=scale(4cm)*unitcircle;

draw(cle);

for(real i=0; i<=length(cle); i+=.2)
  draw(point(cle,i)--2cm*dir(cle,i)+point(cle,i),Arrow,p=i/length(cle)*red);

đź”—generalities-fig137

Figure generalities 137 Generated with Asymptote

Show generalities/fig1380.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Circle | #Loop/for/while

size(0,0);

path cle=scale(4cm)*reverse(unitcircle);

draw(cle);

for(real i=0; i<=length(cle); i+=.2)
  draw(point(cle,i)--2cm*dir(cle,i)+point(cle,i),Arrow,p=i/length(cle)*red);

đź”—generalities-fig139

Figure generalities 139 Generated with Asymptote

Show generalities/fig1400.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Circle | #Loop/for/while

size(0,0);

path cle=scale(4cm)*reverse(unitcircle);

draw(cle);

for(real i=0; i<=length(cle); i+=.2)
  draw(point(cle,i)--(1cm*I*dir(cle,i))+point(cle,i),Arrow,p=i/length(cle)*red);

đź”—generalities-fig140

Figure generalities 140 Generated with Asymptote

Show generalities/fig1410.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Circle | #Shading

size(6cm,0);

path cle=scale(2)*unitcircle;

radialshade(scale(2)*cle, white, (0,0), 2, yellow, (0,0), 4);
radialshade(cle, white, (1,.5), 0, 0.8*blue, (0,0), 2);

for(real i=0; i<=length(cle); i+=.2)
  draw(point(cle,i)--(-2*I*dir(cle,i)+point(cle,i)),p=2mm+yellow+linecap(0));

đź”—generalities-fig146

Figure generalities 146 Generated with Asymptote

Show generalities/fig1470.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Transform/scale/shift/rotate | #Circle

size(0,0);

path p= scale(3cm)*unitcircle;

draw(p,red+1mm);
draw(shift(1mm,2mm)*p);
draw(shift(2*(1mm,2mm))*p);
draw(shift(3*(1mm,2mm))*p);
draw(shift(4*(1mm,2mm))*p);
draw(shift(5*(1mm,2mm))*p);

đź”—generalities-fig151

Figure generalities 151 Generated with Asymptote

Show generalities/fig1520.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Transform/scale/shift/rotate | #Circle

size(8cm,0);

transform scale(pair center, real k)
{
  return shift(center)*scale(k)*shift(-center);
}

path cle=unitcircle;
pair A=(4,0);
draw(cle);

draw(scale(A,.5)*cle,red);
draw(scale(A,-.75)*cle,blue);

for (real t; t<length(cle); t+=1)
  draw(point(cle,t)--point(scale(A,-.75)*cle,t),dotted);

dot("$A$",A,N);

đź”—generalities-fig152

Figure generalities 152 Generated with Asymptote

Show generalities/fig1530.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Transform/scale/shift/rotate | #Circle | #Function creation

size(0,0);

pair inversion(pair O, real k, pair M)
{
  return (O + k*unit(M-O)/abs(M-O));
}

guide inversion(pair O, real k, path M)
{
  guide opath=inversion(O,k,point(M,0));
  for (real i=0; i<=length(M); i+=length(M)/100)
    opath = opath .. inversion(O,k,point(M,i));
  return opath .. cycle;
}

real u=10cm;
path [] p;
path A = scale(u)*unitcircle;
path B = scale(3)*A;
pair z = rotate(10)*(5u,0);


draw(inversion( z, 2*u^2, A ),linewidth(1pt));
draw(inversion( z, 2*u^2, B ),linewidth(1pt));

p[0] = shift(2u,0)*scale(u)*unitcircle;

for (int i=0; i<=5; ++i)
  {
    if (i!=0) p[i] = rotate(360/6)*p[i-1];
    draw(inversion( z, 2 (u^2), p[i] ));
  }

đź”—generalities-fig161

Figure generalities 161 Generated with Asymptote

Show generalities/fig1620.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Circle | #Loop/for/while | #Function creation

size(6cm,0);

pair A=2expi(pi/2);

pair homography(pair z)
{
  return (z^2+A)/(z+2);
}

guide image;
pair tpt;

draw(unitcircle);
for(real t=0; t<length(unitcircle);t+=.05)
  {
    tpt=homography(point(unitcircle,t));
    image=image..tpt;
    draw(point(unitcircle,t)--tpt,dotted);
  }
draw(image..cycle,red);

đź”—generalities-fig176

Figure generalities 176 Generated with Asymptote

Show generalities/fig1770.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Circle | #Intersection | #Function creation

size(6cm,0);

import math;

pair A=(0,0), B=(1,.5);
path cle=shift(1.75,2.5)*unitcircle;
pair pt, ptp;

pair project(pair pt, pair A, pair B)
  {
    return extension(pt,pt-dir(90+degrees(A-B,false)),A,B);
  }

draw(A--B);
draw(cle);

for (real t=0; t<=4; t+=.01)
  {
    pt=point(cle,t);
    ptp=project(pt,A,B);
    dot(ptp, red);
    draw(pt--ptp,dotted);

  }

đź”—generalities-fig178

Figure generalities 178 Generated with Asymptote

Show generalities/fig1790.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Circle | #Geometry | #Intersection

size(6cm,0);

import math;

pair A=(0,0), B=(1,.5), C=(.25,1);

pair ccenter(pair A, pair B, pair C)
  {
    pair mAB=midpoint(A--B);
    pair mAC=midpoint(A--C);
    return extension(mAB, rotate(90,mAB)*A, mAC, rotate(90,mAC)*A);
  }

draw(A--B--C--cycle);

pair circ=ccenter(A,B,C);
pair mAB=midpoint(A--B);
pair mAC=midpoint(A--C);
pair mBC=midpoint(B--C);

dot(circ, red);
dot(mAB^^mAC^^mBC);
drawline(mAB, circ, dotted);
drawline(mAC, circ, dotted);
drawline(mBC, circ, dotted);
draw(shift(circ)*scale(abs(circ-A))*unitcircle);

đź”—generalities-fig179

Figure generalities 179 Generated with Asymptote

Show generalities/fig1800.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Circle | #Geometry | #Intersection

size(6cm,0);

import math;

pair A=(0,0), B=(1,.5), C=(.25,1);

pair project(pair pt, pair A, pair B)
  {
    return extension(pt,pt-dir(90+degrees(A-B,false)),A,B);
  }

pair icenter(pair A, pair B, pair C)
  {
    return extension(A, A+dir(A--B,A--C), B, B+dir(B--A,B--C));
  }

draw(A--B--C--cycle);

pair ins=icenter(A,B,C);
pair iAB=project(ins,A,B);
pair iAC=project(ins,A,C);
pair iBC=project(ins,B,C);

dot(ins, red);
dot(iAB^^iAC^^iBC);
drawline(A, ins, dotted);
drawline(B, ins, dotted);
drawline(C, ins, dotted);
draw(shift(ins)*scale(abs(ins-iAB))*unitcircle);

đź”—generalities-fig180

Figure generalities 180 Generated with Asymptote

Show generalities/fig1810.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Circle | #Geometry | #Intersection | #Function creation

size(6cm,0);
import math;

pair project(pair pt, pair A, pair B)
  {
    return extension(pt,pt-dir(90+degrees(A-B,false)),A,B);
  }


pair ecenter(pair A, pair B, pair C)
  {
    return extension(A, A+rotate(90)*dir(A--B,A--C), B, B+rotate(90)*dir(B--A,B--C));
  }

path ecircle(pair A, pair B, pair C)
  {
    return shift(ecenter(A,B,C))*scale(abs(ecenter(A,B,C)-project(ecenter(A,B,C),B,C)))*unitcircle;
  }

pair A=(0,0), B=(3,0), C=(3,4);
path tr=A--B--C--cycle;

draw(ecircle(A,B,C));
draw(ecircle(B,C,A));

pen p=linewidth(1pt);
drawline(A,B, p);
drawline(A,C, p);
drawline(B,C, p);

đź”—generalities-fig187

Figure generalities 187 Generated with Asymptote

Show generalities/fig1890.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Intersection | #Buildcycle | #Transform/scale/shift/rotate | #Circle

size(6cm,0);
path [] c;

c[1] = xscale(2)*unitcircle;
c[2] = shift((0,1))*c[1];
draw(c[1]^^c[2]);
draw(buildcycle(c[1],c[2]), .8red+4bp);

đź”—generalities-fig189

Figure generalities 189 Generated with Asymptote

Show generalities/fig1910.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Intersection | #Buildcycle | #Transform/scale/shift/rotate | #Circle | #Fill/Unfill

size(8cm,0);

path a,b,c;
a = shift(1,0)*scale(2)*unitcircle;
b = rotate(120)*a;
c = rotate(120)*b;

fill(a, red);
fill(b, green);
fill(c, blue);
fill(buildcycle(a,b), red + green);
fill(buildcycle(b,c), green + blue);
fill(buildcycle(c,a), blue + red);
fill(buildcycle(a,b,c), white);

draw(a^^b^^c);

đź”—generalities-fig190

Figure generalities 190 Generated with Asymptote

Show generalities/fig1920.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Circle | #Fill/Unfill

size(0,0);

path pt1=scale(2cm)*unitcircle;
path pt2=scale(1cm)*unitcircle;

filldraw(pt1^^pt2,yellow+.9white);

đź”—generalities-fig191

Figure generalities 191 Generated with Asymptote

Show generalities/fig1930.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Intersection | #Transform/scale/shift/rotate | #Circle

size(0,0);

path pt1=scale(2cm)*unitcircle;
path pt2=scale(1cm)*unitcircle;

filldraw(pt1^^pt2,evenodd+yellow+.9white);

đź”—generalities-fig192

Figure generalities 192 Generated with Asymptote

Show generalities/fig1940.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Intersection | #Transform/scale/shift/rotate | #Circle

size(0,0);

path pt1=scale(2cm)*unitcircle;
path pt2=scale(1cm)*unitcircle;
path pt3=shift(0,.5cm)*pt2;

filldraw(pt1^^pt2^^pt3,evenodd+yellow+.9white);

đź”—generalities-fig193

Figure generalities 193 Generated with Asymptote

Show generalities/fig1950.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Intersection | #Transform/scale/shift/rotate | #Circle

size(0,0);

path pt1=scale(2cm)*unitcircle;
path pt2=scale(1cm)*unitcircle;
path pt3=shift(0,1.5cm)*pt2;

filldraw(pt1^^pt2^^pt3,evenodd+yellow+.9white);

đź”—geometry-fig027

Figure geometry 027 Generated with Asymptote

Show geometry/fig0270.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Circle | #Ellipse | #Path

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((0,0),i=(1,1),j=(-0.5,.75));
show("","$\vec{u}$", "$\vec{v}$", currentcoordsys, ipen=blue);
show(defaultcoordsys);

point A=(0,0);

real R=2;
/*<asyxml><view file="modules/geometry.asy" type="" signature="struct circle"/></asyxml>*/
circle C=circle(A,R);
draw(C,1.5mm+red);

circle Cp=circle(point(defaultcoordsys,A),R);
draw(Cp,0.75mm+blue);

// One can draw in the 'currentcoordsys' a circle definided in
// the 'defaultcoordsys'
/*<asyxml><view file="modules/geometry.asy" type="path" signature="*(coordsys,path)"/></asyxml>*/
draw(currentcoordsys*Cp, red+blue);

đź”—geometry-fig028

Figure geometry 028 Generated with Asymptote

Show geometry/fig0280.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Point | #Clip | #Circle

import geometry;
size(10cm);

// currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-0.25,0.75));
// show(currentcoordsys);

point A=(-1,0), B=(2,0), C=(0,2);

draw(line(A,B), linewidth(bp));
draw(line(A,C), linewidth(bp));
draw(line(B,C), linewidth(bp));

/*<asyxml><view file="modules/geometry.asy" type="circle" signature="circle(point,point,point)"/></asyxml>*/
circle cc=circle(A,B,C);
draw(cc, blue);
dot(cc.C, blue);

/*<asyxml><view file="modules/geometry.asy" type="circle" signature="incircle(point,point,point)"/></asyxml>*/
circle ic=incircle(A,B,C);
draw(ic, red);
dot(ic.C, red);


/*<asyxml><view file="modules/geometry.asy" type="circle" signature="excircle(point,point,point)"/></asyxml>*/
circle ec=excircle(A,B,C);
/*<asyxml><view file="modules/geometry.asy" type="void" signature="clipdraw(picture,Label,path,align,pen,arrowbar,arrowbar,real,real,Label,marker)"/></asyxml>*/
clipdraw(ec, green);
dot(ec.C, green);

ec=excircle(A,C,B);
clipdraw(ec, green);
dot(ec.C, green);

ec=excircle(C,B,A);
clipdraw(ec, green);
dot(ec.C, green);

dot("G",centroid(A,B,C),NE);

// Enlarge the bounding box of the current picture
// draw(box((-2.5,-3), (3.5,3.5)));

đź”—geometry-fig029

Figure geometry 029 Generated with Asymptote

Show geometry/fig0290.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Transform/scale/shift/rotate | #Ellipse | #Circle

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-0.25,.75));
show(currentcoordsys);

point A=(1,1);
dot("$A$",A,S,red);

real R=2;
circle C=circle(A,R);
draw(C,Arrow);

/*<asyxml><view file="modules/geometry.asy" type="ellipse" signature="*(transform,circle)"/></asyxml>*/
ellipse el=xscale(2)*C;
draw(el,blue,Arrow);

// /*<asyxml><view file="modules/geometry.asy" type="transform" signature="xscale(real,point)"/></asyxml>*/
ellipse el=xscale(2,A)*C;
draw(el,red,Arrow);

đź”—geometry-fig030

Figure geometry 030 Generated with Asymptote

Show geometry/fig0300.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Transform/scale/shift/rotate | #Ellipse | #Circle

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-0.25,.75));
show(currentcoordsys);

point A=(1,1);
dot("$A$",A,S,red);

real R=2;
circle C=circle(A,R);
draw(C,Arrow);

/*<asyxml><view file="modules/geometry.asy" type="ellipse" signature="*(transform,circle)"/></asyxml>*/
draw(scale(0.5)*C,red,Arrow);

draw(scale(0.5,A)*C,2mm+0.8*blue);

/*<asyxml><view file="modules/geometry.asy" type="circle" signature="/(explicit circle,real)"/></asyxml>*/
draw(C/2,0.75mm+green,Arrow(4mm));

// Note that the point 'point(C,0)' is always at the same place relatively to 'C'.
draw(rotateO(180)*C/2,0.8*yellow,Arrow);

đź”—geometry-fig031

Figure geometry 031 Generated with Asymptote

Show geometry/fig0310.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Transform/scale/shift/rotate | #Ellipse | #Circle

import geometry;
size(10cm,0);

currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-0.25,.75));
show(currentcoordsys);

point A=(1,1);
dot("$A$",A,S,red);

real a=3, b=2;
ellipse el=ellipse(A,a,b,0);
draw(el,Arrow);

/*<asyxml><view file="modules/geometry.asy" type="ellipse" signature="*(transform,ellipse)"/></asyxml>*/
draw(scale(0.5)*el,red,Arrow);

draw(scale(0.5,A)*el,2mm+0.8*blue);

/*<asyxml><view file="modules/geometry.asy" type="ellipse" signature="/(ellipse,real)"/></asyxml>*/
draw(el/2,0.75mm+green,Arrow(4mm));

// Note that the point 'point(el,0)' is always at the same place relatively to 'el'.
draw(rotateO(135)*el/2,0.8*yellow,Arrow);

đź”—geometry-fig035

Figure geometry 035 Generated with Asymptote

Show geometry/fig0350.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Circle | #Line | #Intersection

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-0.25,.75));
show(currentcoordsys, xpen=invisible);

point A=(-1,0);
point B=(0.5,-3sin(2));
dot("$A$",A,S,red);
dot("$B$",B,N,red);

line l=line(A,B);
circle c=circle((point)(0,-sqrt(2)/2),exp(1));
draw(l);
draw(c);

/*<asyxml><view file="modules/geometry.asy" type="point[]" signature="intersectionpoints(line,circle)"/></asyxml>*/
point[] inter=intersectionpoints(l,c);
dot("$M$", inter[0], 2S, red);
dot("$N$", inter[1], 2N+0.5W, red);

đź”—geometry-fig039

Figure geometry 039 Generated with Asymptote

Show geometry/fig0390.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Line | #Intersection | #Circle

import geometry;

size(8cm,0);

currentcoordsys=cartesiansystem((0,0),i=(1,1),j=(-0.5,.75));
show(currentcoordsys);

point A=(-0.5,.75);
point B=(1,1);
dot("$A$",A,SE);
dot("$B$",B,NW);

line l=line(A,B,false);
line ll=hline()+B;

circle c=circle((point)(0.5,0.5),2);
draw(l^^ll);
draw(complementary(l),dashed+grey);
draw(c);

dotfactor*=2;

/*<asyxml><view file="modules/geometry.asy" type="point[]" signature="intersectionpoints(line,circle)"/></asyxml>*/
dot(intersectionpoints(l,c),red);
dot(intersectionpoints(ll,c),red);

đź”—geometry-fig042

Figure geometry 042 Generated with Asymptote

Show geometry/fig0420.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Line | #Intersection | #Circle

import geometry;
size(10cm,0);

// currentcoordsys=cartesiansystem((0,0),i=(1,1),j=(-0.5,.75));
// show(currentcoordsys);

point A=(-1,-1);
point B=(0.75,0.5);
dot("$A$",A,NW,red);
dot("$B$",B,N,red);

circle c1=circle(A,1.5);
circle c2=circle(B,2);
draw(c1^^c2);

/*<asyxml><view file="modules/geometry.asy" type="line" signature="radicalline(circle,circle)"/></asyxml>*/
draw(radicalline(c1,c2));
/*<asyxml><view file="modules/geometry.asy" type="point" signature="radicalcenter(circle,circle)"/></asyxml>*/
dot(radicalcenter(c1,c2));

dotfactor*=2;

/*<asyxml><view file="modules/geometry.asy" type="point[]" signature="intersectionpoints(circle,circle)"/></asyxml>*/
point[] inter=intersectionpoints(c1,c2);
dot("$M$", inter[0], 2SW, red);
dot("$N$", inter[1], 2NE, red);

đź”—geometry-fig044

Figure geometry 044 Generated with Asymptote

Show geometry/fig0440.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Line | #Intersection | #Circle | #Tangent

import geometry;
size(10cm,0);

// currentcoordsys=cartesiansystem((0,0),i=(1,0.25),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(-1,-1);
point B=(0.75,0.5);
dot("$A$",A,NW,red);
dot("$B$",B,N,red);

circle c1=circle(A,1.5);
circle c2=circle(B,2);
draw(c1^^c2);

point[] inter=intersectionpoints(c1,c2);
dot("$M$", inter[0], 2NW, red);

/*<asyxml><view file="modules/geometry.asy" type="line" signature="tangent(circle,point)"/></asyxml>*/
draw(tangent(c1,inter[0]), grey);
draw(tangent(c2,inter[0]), grey);

/*<asyxml><view file="modules/geometry.asy" type="line" signature="tangent(circle,abscissa)"/></asyxml>*/
draw(tangent(c2,angabscissa(135)), grey);

đź”—geometry-fig045

Figure geometry 045 Generated with Asymptote

Show geometry/fig0450.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Line | #Intersection | #Circle | #Point | #Perpendicular

import geometry;
size(10cm,0);

point c2=(13,5);
real r=4, R=abs(c2)-r;

circle[] C={circle(origin, 4), circle(c2,R)};
draw(C[0]^^C[1], blue);

segment s=segment(origin, c2);
draw(s, red, dot);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="curpoint(line,real)"/></asyxml>*/
point T=curpoint(s,r/(r-R)*abs(c2));
dot(T);
/*<asyxml><view file="modules/geometry.asy" type="line" signature="tangents(circle,point)"/></asyxml>*/
line[] tgt=tangents(C[1], T);
draw(tgt);

point[][] t= new point[2][2];
for (int i=0; i < 2 ; ++i)
  for (int j=0; j < 2; ++j) {
    /*<asyxml><view file="modules/geometry.asy" type="point[]" signature="intersectionpoints(line,circle)"/></asyxml>*/
    t[i][j]=intersectionpoints(C[i],tgt[j])[0];
    draw(C[i].C--t[i][j], dot);
    markrightangle(T, t[i][j], C[i].C, size=(i == 0 ? 2mm : 0));
  }

addMargins(cm/2,cm/2);

đź”—geometry-fig050

Figure geometry 050 Generated with Asymptote

Show geometry/fig0500.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Line | #Intersection | #Circle | #Tangent | #Point

import geometry;
size(10cm,0);

currentcoordsys=cartesiansystem((0,0),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(2.5,-1);
point B=A+(3,1);
dot("$A$",A,SW);
dot("$B$",B,2N+0.5W);

circle c1=circle(A,1.5);
draw(c1);

/*<asyxml><view file="modules/geometry.asy" type="line[]" signature="tangents(circle,point)"/></asyxml>*/
line[] tgt=tangents(c1,B);
draw(tgt,red);
/*<asyxml><view file="modules/geometry.asy" type="circle" signature="circle(point,point)"/></asyxml>*/
draw(circle(B,A),grey);

// dot(intersectionpoints(c1,circle(B,A)),red);
for (int i=0; i<tgt.length; ++i) {
  dot(intersectionpoints(c1,tgt[i]),2mm+red);
}

đź”—geometry-fig051

Figure geometry 051 Generated with Asymptote

Show geometry/fig0510.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Line | #Intersection | #Circle | #Tangent | #Ellipse | #Point

import geometry;
size(12cm,0);

// currentcoordsys=cartesiansystem((0,0),i=(1,0.5),j=(-0.5,.75));
// show(currentcoordsys, xpen=invisible);

point A=(2.5,-1);
dot("$A$",A,SW);
ellipse el1=ellipse(A,2,1,10);
draw(el1);

circle C=circle(A,3);
draw(C);
for (int i=0; i < 360; i+=90) {

  point B=point(C,angabscissa(i));
  dot("$B$",B,locate(unit(B-A)));


  line[] tgt=tangents(el1,B);
  draw(tgt,0.8*red);

  for (int i=0; i < tgt.length; ++i) {
    dot(intersectionpoints(el1,tgt[i]),blue);
  }

}

đź”—geometry-fig052

Figure geometry 052 Generated with Asymptote

Show geometry/fig0520.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Line | #Intersection | #Circle | #Tangent | #Ellipse | #Point

import geometry;
size(12cm,0);

// currentcoordsys=cartesiansystem((0,0),i=(1,0.5),j=(-0.5,.75));
// show(currentcoordsys, xpen=invisible);

point F=(0,0);
dot("$F$", F, SW);
parabola p=parabola(F, 0.1, 30);
draw(p);

point C=shift(2*(p.V-p.F))*p.V;
circle cle=circle(C, 0.2);
draw(cle);
for (int i=0; i < 360; i+=90) {

  point M=point(cle, angabscissa(i));
  dot("$M$", M, locate(unit(M-C)));

  line[] tgt=tangents(p, M);
  draw(tgt, 0.8*red);

  for (int i=0; i < tgt.length; ++i) {
    dot(intersectionpoints(p, tgt[i]), blue);
  }
}

đź”—geometry-fig053

Figure geometry 053 Generated with Asymptote

Show geometry/fig0530.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Coords system | #Circle | #Point

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((0,0),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(-0.5,-0.5);
point B=(1,0.5);
point C=(0.5,1);
dot("$A$",A,SW);
dot("$B$",B,2N+0.5W);
dot("$C$",C,2N+0.5W);

/*<asyxml><view file="modules/geometry.asy" type="circle" signature="circle(point,point,point)"/></asyxml>*/
circle c1=circle(A,B,C);
dot("$\Omega$",c1.C,N);
draw(c1);

đź”—geometry-fig057

Figure geometry 057 Generated with Asymptote

Show geometry/fig0570.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Distance | #Circle | #Abscissa | #Point

import geometry;
size(10cm,0);

currentcoordsys=cartesiansystem((0,0),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(2,-2);
dot("$A$",A,S,red);

circle C=circle(A,2);
draw(C);
/*<asyxml><view file="modules/geometry.asy" type="void" signature="distance(picture pic,Label,point,point,bool,real,pen,pen,arrow)"/></asyxml>*/
distance("$R=2$",A,point(C,0),0);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="relpoint(explicit circle,real)"/></asyxml>*/
dot("relpoint(C, 0)",relpoint(C,0),E);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(circle,abscissa)"/></asyxml>*/
dot("relpoint(C, 0.25)",point(C,Relative(0.25)),NW);
// point(C,Relative(0.25)) can be replaced by relpoint(C,0.25) OR point(C,relabscissa(0.25))

dot("relpoint(C, 0.5)",relpoint(C,0.5),W);
dot("relpoint(C, 0.75)",relpoint(C,0.75),SE);
dot("relpoint(C, 1.125)",relpoint(C,1.125),NE);

đź”—geometry-fig060

Figure geometry 060 Generated with Asymptote

Show geometry/fig0600.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Circle | #Abscissa | #Point

import geometry;
size(11cm,0);

currentcoordsys=cartesiansystem((0,0),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(2,-2);
dot("$A$",A,S,red);

circle C=circle(A,2);
draw(C);
distance("$R=2$",A,point(C,0),0);

/*<asyxml><view file="modules/geometry.asy" type="pair" signature="curpoint(explicit circle,real)"/></asyxml>*/
dot("curpoint(C, pi/2)", curpoint(C,pi/2),NE);

dot("curpoint(C, -pi/2)", curpoint(C,-pi/2));

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="curabscissa(real)"/></asyxml>*/
dot("curpoint(C, pi)", point(C,curabscissa(pi)),NW);
// point(C,curabscissa(pi)) can be replaced by curpoint(C,pi)

dot("curpoint(C, 2*pi)", curpoint(C,2*pi),W);
dot("curpoint(C, 3*pi)", curpoint(C,3*pi),SE);
dot("curpoint(C, 4.25*pi)", curpoint(C,4.25*pi),E);

đź”—geometry-fig063

Figure geometry 063 Generated with Asymptote

Show geometry/fig0630.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Circle | #Abscissa | #Point

import geometry;
size(11cm,0);

currentcoordsys=cartesiansystem((0,0),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(2,-2);
dot("$A$",A,S,red);

circle C=circle(A,2);
draw(C);
distance("$R=2$",A,point(C,0),0);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="angpoint(explicit circle,real)"/></asyxml>*/
dot("angpoint(C, 90)", angpoint(C,90),NW);

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="angabscissa(real,polarconicroutine)"/></asyxml>*/
dot("angpoint(C, 180)", point(C,angabscissa(180)), W);
// point(C,angabscissa(180)) can be replaced by angpoint(C,180)

dot("angpoint(C, 270)", angpoint(C,270),SE);
dot("angpoint(C, 405)", angpoint(C,405),NE);
dot("angpoint(C, -45)", angpoint(C,-45),SE);

đź”—geometry-fig069

Figure geometry 069 Generated with Asymptote

Show geometry/fig0690.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Abscissa | #Circle | #Point

import geometry;
size(10cm,0);

// currentcoordsys=cartesiansystem((0,0),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(4,2);
dot("$A$",A,S,red);

real R=2;
circle C=circle(A,R);
draw(C,linewidth(1mm));
draw("$R="+(string)R+"$", A--point(C,0), N, Arrows);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(explicit circle,explicit real)"/></asyxml>*/
dot("point(C, 15)", point(C,15),2E,3mm+blue);

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="nodabscissa(real)"/></asyxml>*/
dot("point(C, 40)",
    point(C,nodabscissa(40)),
    2W,3mm+blue);
// point(C,nodabscissa(40)) can be replaced by point(C,40)

/*<asyxml><view file="modules/geometry.asy" type="int" signature="circlenodesnumber(real)"/></asyxml>*/
dot("point(C, 3*circlenodesnumber(R)/4)",
    point(C, 3*circlenodesnumber(R)/4), S, 3mm+blue);

dot((path)C, yellow);

write(length((path)C));

đź”—geometry-fig073

Figure geometry 073 Generated with Asymptote

Show geometry/fig0730.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Abscissa | #Circle | #Point

import geometry;
unitsize(2cm);

// currentcoordsys=cartesiansystem((0,0),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(-2,2);
dot("$A$",A,S);
point B=A+(cos(0.5),cos(1));
dot("$B$",B,S);


circle c=circle(A,2);
draw(c);

line l=line(A,B);
draw(l);
point M=intersectionpoints(l,c)[0];
point P=intersectionpoints(l,c)[1];

/*<asyxml><view file="modules/geometry.asy" type="void" signature="dot(picture,Label,explicit point,align,string,pen)"/></asyxml>*/
dot("",M,2E,linewidth(2mm));
dot("$M$",M,2W);
dot("",P,2E,linewidth(2mm));
dot("$P$",P,2W);

pair p=A-(4,2.5);
transform t=shift((0,-0.3));
transform T=shift((4,0));
real x;

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="angabscissa(circle,point)"/></asyxml>*/
x=angabscissa(c,M).x;
label("angabscissa(c,M).x=$"+(string)x+"^\circ$",p,E);
dot(angpoint(c,x),1mm+red);
x=angabscissa(c,P).x;
label("angabscissa(c,P).x=$"+(string)x+"^\circ$",T*p,E);
dot(angpoint(c,x),1mm+red);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="curabscissa(circle,point)"/></asyxml>*/
x=curabscissa(c,M).x;
dot(curpoint(c,x),1mm+red);
label("curabscissa(c,M).x="+(string)x,p,E);
x=curabscissa(c,P).x;
label("curabscissa(c,P).x="+(string)x,T*p,E);
dot(curpoint(c,x),1mm+red);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="nodabscissa(circle,point)"/></asyxml>*/
x=nodabscissa(c,M).x;
label("nodabscissa(c,M).x="+(string)x,p,E);
dot(point(c,x),1mm+red);
x=nodabscissa(c,P).x;
label("nodabscissa(c,P).x="+(string)x,T*p,E);
dot(point(c,x),1mm+red);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="relabscissa(circle,point)"/></asyxml>*/
x=relabscissa(c,M).x;
label("relabscissa(c,M).x="+(string)x,p,E);
dot(relpoint(c,x),1mm+red);
x=relabscissa(c,P).x;
label("relabscissa(c,P).x="+(string)x,T*p,E);
dot(relpoint(c,x),1mm+red);

đź”—geometry-fig076

Figure geometry 076 Generated with Asymptote

Show geometry/fig0760.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Ellipse | #Draw (2D) | #Circle | #Parabola | #Hyperbola | #Conic | #Intersection

import geometry;
size(12cm);

// currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-0.25,0.75));
// currentcoordsys=cartesiansystem((2,1),i=rotate(45)*(1,0),j=rotate(45)*(0,1));
// show(currentcoordsys);

conic co[];
co[0]=circle((point)(0,0),1);
/*<asyxml><view file="modules/geometry.asy" type="void" signature="draw(picture,Label,explicit conic,align,pen,arrowbar,arrowbar,margin,Label,marker)"/></asyxml>*/
draw(co[0]);

co[1]=ellipse((point)(0,0),4,1);
draw(co[1]);

co[2]=parabola((0,0),1,90);
draw(co[2]);

hyperbola h=hyperbola((-1,0),(1,0),1.2,byvertices);
co[3]=h;
draw(co[3]);
draw(h.A1,grey);
draw(h.A2,grey);

dotfactor *= 1;

for (int i=0; i < 4; ++i) {
  dot(intersectionpoints(h.A1,co[i]),blue);
  dot(intersectionpoints(h.A2,co[i]),blue);
  for (int j=i+1; j < 4; ++j)
    /*<asyxml><view file="modules/geometry.asy" type="point[]" signature="intersectionpoints(conic,conic)"/></asyxml>*/
    dot(intersectionpoints(co[i],co[j]), red);
}

đź”—geometry-fig077

Figure geometry 077 Generated with Asymptote

Show geometry/fig0770.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Ellipse

import geometry;
size(8cm);

currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
// show(currentcoordsys, xpen=invisible);

point A=(-1,0) ; dot("$A$",A,S);
point B=(1,1)  ; dot("$B$",B,S);
point C=(0,1)  ; dot("$C$",C,SW);
point D=(1,-1) ; dot("$D$",D,SW);

circle c=circle(origin(),2);

line l1=line(A,B); draw(l1);
line l2=line(C,D); draw(l2);

point[] J=intersectionpoints(l1,c);
point[] K=intersectionpoints(l2,c);

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="arc(ellipse,point,point,bool)"/></asyxml>*/
draw(arc(c,J[0],K[0]),1mm+0.8yellow);
draw(arc(c,K[0],J[1]),1mm+0.8red);
/*<asyxml><view file="modules/geometry.asy" type="arc" signature="arc(ellipse,abscissa,abscissa,bool)"/></asyxml>*/
draw(arc(c,angabscissa(c,J[1]),angabscissa(c,K[1])),1mm+0.8blue);
draw(arc(c,angabscissa(c,K[1]),angabscissa(c,J[0])),1mm+0.8green);

dot("$J_0$",J[0],2W); dot("$J_1$",J[1],2N);
dot("$K_0$",K[0],2E) ; dot("$K_1$",K[1],2N+W);

đź”—geometry-fig078

Figure geometry 078 Generated with Asymptote

Show geometry/fig0780.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Ellipse

import geometry;
size(8cm);

// currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
// show(currentcoordsys, xpen=invisible);

point A=(-1,0) ; dot("$A$",A,S);
point B=(1,1)  ; dot("$B$",B,S);
point C=(0,1)  ; dot("$C$",C,SW);
point D=(1,-1) ; dot("$D$",D,SW);

ellipse el=ellipse((point)(0,0.5),2,1);

line l1=line(A,B); draw(l1);
line l2=line(C,D); draw(l2);

point[] J=intersectionpoints(l1,el);
point[] K=intersectionpoints(l2,el);

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="arc(ellipse,point,point,bool)"/></asyxml>*/
draw(arc(el, J[0],K[0]), 1mm+0.8yellow);
draw(arc(el, K[0],J[1]), 1mm+0.8red);
/*<asyxml><view file="modules/geometry.asy" type="arc" signature="arc(ellipse,abscissa,abscissa,bool)"/></asyxml>*/
draw(arc(el,angabscissa(el,J[1]), angabscissa(el,K[1])), 1mm+0.8blue);
draw(arc(el,angabscissa(el,K[1]), angabscissa(el,J[0])), 1mm+0.8green);

dot("$J_0$", J[0], 2N); dot("$J_1$", J[1], 2S);
dot("$K_0$", K[0], 2NE) ; dot("$K_1$", K[1], 2dir(-35));

đź”—geometry-fig079

Figure geometry 079 Generated with Asymptote

Show geometry/fig0790.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle

import geometry;
size(6cm);

// currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
// show(currentcoordsys, xpen=invisible);

point A=(-1,0);
point B=(3,-1);
point C=(0,1);

circle cle=circle(A,C,B);
draw(cle,linewidth(2mm));

draw(arc(cle,A,B), dotsize()+red);
draw(arc(cle,A,B,CW), dotsize()+blue);

dot(Label("$A$", black), A, 1.5NW, white);
dot(Label("$B$", black), B, E, white);
dot(Label("$C$", black), C, NW, white);

đź”—geometry-fig080

Figure geometry 080 Generated with Asymptote

Show geometry/fig0800.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Ellipse | #Transform/scale/shift/rotate

import geometry;
size(8cm,0);

// currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(1,1);
dot("$A$",A,S,0.8red);

real R=2;
/*<asyxml><view file="modules/geometry.asy" type="" signature="struct arc"/></asyxml>*/
arc C=arc(circle(A,R),45,180);/*<asyxml><view file="modules/geometry.asy" type="arc" signature="arc(ellipse,real,real,polarconicroutine,bool)"/></asyxml>*/
draw(C,Arrow);

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="complementary(arc)"/></asyxml>*/
draw(complementary(C),dashed+grey,Arrow(position=Relative(0.75)));

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="*(transform,explicit arc)"/></asyxml>*/
arc Cp=scale(0.5,A)*C;
draw(Cp,0.8red,Arrow);

arc Cp=scale(-0.5,A)*C;
draw(Cp,0.8blue,Arrow);

arc Cp=scale(1.1,A)*C;
/*<asyxml><view file="modules/geometry.asy" type="arc" signature="reverse(arc)"/></asyxml>*/
draw(reverse(Cp),0.8*yellow,Arrow);

arc Cp=scale(0.9,A)*C;
draw(rotate(225,A)*Cp,0.8green,Arrow);

đź”—geometry-fig081

Figure geometry 081 Generated with Asymptote

Show geometry/fig0810.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Ellipse | #Transform/scale/shift/rotate

import geometry;
size(8cm,0);

// currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(1,1);
dot("$A$",A,S,0.8red);

real R=2;
/*<asyxml><view file="modules/geometry.asy" type="" signature="struct arc"/></asyxml>*/
arc C=arc(ellipse(A,2R,R),45,180,fromCenter);
draw(C,Arrow);

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="complementary(arc)"/></asyxml>*/
draw(complementary(C),dashed+grey,Arrow(position=Relative(0.75)));

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="*(transform,explicit arc)"/></asyxml>*/
arc Cp=scale(0.5,A)*C;
draw(Cp,0.8red,Arrow);

arc Cp=scale(-0.5,A)*C;
draw(Cp,0.8blue,Arrow);

arc Cp=scale(1.1,A)*C;
/*<asyxml><view file="modules/geometry.asy" type="arc" signature="reverse(arc)"/></asyxml>*/
draw(reverse(Cp),0.8*yellow,Arrow);

arc Cp=scale(0.9,A)*C;
draw(rotate(225,A)*Cp,0.8green,Arrow);

đź”—geometry-fig082

Figure geometry 082 Generated with Asymptote

Show geometry/fig0820.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Transform/scale/shift/rotate | #Markers

import geometry;
size(8cm,0);

// currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(1,1);
dot("$A$",A,S,red);

real R=2;
arc C=arc(circle(A,R), 45, 210);
draw(C,linewidth(4mm));

/*<asyxml><view file="modules/geometry.asy" type="void" signature="markarc(picture,Label,int,real,real,arc,arrowbar,pen,pen,margin,marker)"/></asyxml>*/
markarc(format("%0g",degrees(C)), C, Arrow);

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="*(real, explicit arc)"/></asyxml>*/
draw(0.5*C,2mm+yellow);

arc Cp=C/3;
draw(Cp,1mm+blue);
markarc(format("%0g",degrees(Cp)), radius=25mm, Cp, blue, Arrow);

đź”—geometry-fig083

Figure geometry 083 Generated with Asymptote

Show geometry/fig0830.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Transform/scale/shift/rotate | #Markers

import geometry;
size(8cm,0);

// currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(1,1);
dot("$A$", A, NW, red);

real R=2;
arc C=arc(circle(A,R), 45, 210, CW);
draw(C,linewidth(4mm));

/*<asyxml><view file="modules/geometry.asy" type="void" signature="markarc(picture,Label,int,real,real,arc,arrowbar,pen,pen,margin,marker)"/></asyxml>*/
markarc(format("%0g",degrees(C)), C, radius=markangleradius(), Arrow);

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="*(real, explicit arc)"/></asyxml>*/
draw(0.5*C, 2mm+yellow);

arc Cp=C/3;
draw(Cp, 1mm+blue);
markarc(format("%0g",degrees(Cp)), radius=-25mm, Cp, blue, Arrow);

đź”—geometry-fig085

Figure geometry 085 Generated with Asymptote

Show geometry/fig0850.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Transform/scale/shift/rotate | #Markers

import geometry;
size(8cm,0);

// currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
// show(currentcoordsys, xpen=invisible);

point C=(1,1);
dot("$C$", C, dir(30), red);

arc a=arc(ellipse(C,2,1,30), -45, 45);
draw(a, linewidth(4mm));
dot("$F_1$", a.el.F1, dir(210), red);

/*<asyxml><view file="modules/geometry.asy" type="void" signature="markarc(picture,Label,int,real,real,arc,arrowbar,pen,pen,margin,marker)"/></asyxml>*/
markarc(format("%0g", degrees(a)), radius=2.5*markangleradius(), a);

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="*(real, explicit arc)"/></asyxml>*/
draw(0.5*a, 2mm+yellow);

arc ap=a/3;
draw(ap, 1mm+blue);
markarc(format("%0g", degrees(ap)), radius=1.5*markangleradius(), ap, blue);

đź”—geometry-fig086

Figure geometry 086 Generated with Asymptote

Show geometry/fig0860.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Abscissa | #Point

import geometry;
size(10cm,0);

// currentcoordsys=cartesiansystem((1,2), i=(1,0.5), j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(1,1);
dot("$A$", A, S, red);

arc C=arc(circle(A,2), 45, 270);
draw(C, Arrow);

/*<asyxml><view file="modules/geometry.asy" type="real" signature="degrees(arc)"/></asyxml>*/
write(degrees(C)); // Output is 225

draw(complementary(C), grey+dashed);
distance("$R=2$",A,point(C,0),0);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="relpoint(arc,real)"/></asyxml>*/
dot("relpoint(C, 0)", relpoint(C,0),E);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(arc,abscissa)"/></asyxml>*/
dot("relpoint(C, 0.25)", point(C,Relative(0.25)),N);// point(C,Relative(0.25)) is similar to relpoint(C,0.25)
dot("relpoint(C, -0.5)", relpoint(C,-0.5),E);
dot("relpoint(C, 0.5)",  relpoint(C,0.5),W);
dot("relpoint(C, 0.75)", relpoint(C,0.75),W);
dot("relpoint(C, 1.25)", relpoint(C,1.25),E);

đź”—geometry-fig088

Figure geometry 088 Generated with Asymptote

Show geometry/fig0880.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Abscissa | #Point

import geometry;
size(10cm,0);

// currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(3.5,0.5);
dot("$A$",A,S,red);

arc C=arc(circle(A,2),45,270,CCW);
draw(C,Arrow);
draw(complementary(C),grey+dashed);
/*<asyxml><view file="modules/geometry.asy" type="void" signature="distance(picture pic,Label,point,point,bool,real,pen,pen,arrow)"/></asyxml>*/
distance("$R=2$",A,point(C.el,0),0);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="curpoint(arc,real)"/></asyxml>*/
dot("curpoint(C, 0)", curpoint(C,0),E);
dot("curpoint(C, pi/2)", curpoint(C,pi/2),N);
dot("curpoint(C, -pi/2)", curpoint(C,-pi/2));

// dot("curpoint(C, pi)", point(C,curabscissa(pi)),W); // OR curpoint(C,pi)
dot("curpoint(C, pi)", curpoint(C,pi),W);

dot("curpoint(C, 2*pi)", curpoint(C,2*pi),SW);
dot("curpoint(C, 3*pi)", curpoint(C,3*pi),E);

đź”—geometry-fig090

Figure geometry 090 Generated with Asymptote

Show geometry/fig0900.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Abscissa | #Point

import geometry;
size(10cm,0);

// currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(3.5,0.5);
dot("$A$", A, S, red);

arc C=arc(circle(A,2), 60, 270, CCW);
draw(C,Arrow);
draw(complementary(C), grey+dashed);
distance("$R=2$",A,point(C.el,0),0);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="angpoint(arc,real)"/></asyxml>*/
dot("angpoint(C, 90)",  angpoint(C,90), W);

dot("angpoint(C, 180)", point(C,angabscissa(180)), SW); // point(C,angabscissa(180)) is similar to angpoint(C,180)

dot("angpoint(C, 270)", angpoint(C,270), E);
dot("angpoint(C, -45)", angpoint(C,-45), E);

đź”—geometry-fig092

Figure geometry 092 Generated with Asymptote

Show geometry/fig0920.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Abscissa | #Point

import geometry;
unitsize(1.5cm);

// currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

real R=2;
point A=(3.5,1.5);

dot("$A$",A,S,red);

arc C=arc(circle(A,2), 45, 270);
draw(C,Arrow);
draw(complementary(C),grey+dashed);
distance("$R=2$",A,point(C,0),0);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="point(arc,real)"/></asyxml>*/
dot("point(C, 15)", point(C,15), 2N, 3mm+blue);

dot("point(C, 30)",
    point(C,nodabscissa(30)), // OR point(C,40)
    2W,3mm+blue);

/*<asyxml><view file="modules/geometry.asy" type="int" signature="arcnodesnumber(explicit arc)"/></asyxml>*/
dot(Label("point(C, 3*arcnodesnumber(R)/4)",UnFill),
    point(C, 3*arcnodesnumber(C)/4), 2E, 3mm+blue);

dot((path)C, yellow);

đź”—geometry-fig094

Figure geometry 094 Generated with Asymptote

Show geometry/fig0940.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Abscissa | #Point

import geometry;
unitsize(2cm);
linemargin=0.5cm;

// currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(3.5,0.75);
dot("$A$",A,S);
point B=A+(cos(0.5),cos(1));
dot("$B$",B,S);


arc c=arc(circle(A,2), 45, 270, CCW);
arc cc=complementary(c);
draw(c,Arrow);
draw(cc,dashed+grey);

line l=line(A,B);
draw(l);
point M=intersectionpoints(l,c)[0];
point P=intersectionpoints(l,cc)[0];

dot("", M, 2E);
dot("$M$", M, 2W, linewidth(2mm));
dot("", P, 2E);
dot("$P$", P, 2W, linewidth(2mm));
dot("$O$", point(c,0), SE);

point p=A-(4,2.5);
transform t=shift((0,-0.3));
transform T=shift((4,0));
real x;

/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="angabscissa(arc,point)"/></asyxml>*/
x=angabscissa(c,M).x;
label("angabscissa(c,M).x=$"+(string)x+"^\circ$",p,E);
dot(angpoint(c,x),1mm+red);
x=angabscissa(c,P).x;
label("angabscissa(c,P).x=$"+(string)x+"^\circ$",T*p,E);
dot(angpoint(c,x),1mm+red);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="curabscissa(arc,point)"/></asyxml>*/
x=curabscissa(c,M).x;
dot(curpoint(c,x),1mm+red);
label("curabscissa(c,M).x="+(string)x,p,E);
x=curabscissa(c,P).x;
label("curabscissa(c,P).x="+(string)x,T*p,E);
dot(curpoint(c,x),1mm+red);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="nodabscissa(arc,point)"/></asyxml>*/
x=nodabscissa(c,M).x;
label("nodabscissa(c,M).x="+(string)x,p,E);
dot(point(c,x),1mm+red);
label("nodabscissa(c,P).x= \scriptsize{ERROR (point is not on the arc!)}",T*p,E);

p=t*p;
/*<asyxml><view file="modules/geometry.asy" type="abscissa" signature="relabscissa(arc,point)"/></asyxml>*/
x=relabscissa(c,M).x;
label("relabscissa(c,M).x="+(string)x,p,E);
dot(relpoint(c,x),1mm+red);
x=relabscissa(c,P).x;
label("relabscissa(c,P).x="+(string)x,T*p,E);
dot(relpoint(c,x),1mm+red);

đź”—geometry-fig096

Figure geometry 096 Generated with Asymptote

Show geometry/fig0960.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Line | #Abscissa | #Intersection | #Point

import geometry;
size(8cm);

// currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(-1,0) ; dot("$A$",A,S);
point B=(1,1)  ; dot("$B$",B,S);
point C=(0,0)  ;
point D=(1,-1) ; dot("$D$",D,SW);

arc c=arc(circle(C,2), 0, 270);
draw(complementary(c),dashed+grey);

line l1=line(A,B); draw(l1);
line l2=line(C,D); draw(l2);

point[] J=intersectionpoints(l1,c);
point[] K=intersectionpoints(l2,c);

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="arc(explicit arc,point,point)"/></asyxml>*/
draw(arc(c,K[0],J[0]),2mm+0.8yellow);
draw(arc(c,J[1],K[0]),2mm+0.8red);
/*<asyxml><view file="modules/geometry.asy" type="arc" signature="arc(explicit arc,abscissa,abscissa)"/></asyxml>*/
draw(arc(c,relabscissa(c,J[0]),relabscissa(1)),2mm+0.8green);
draw(arc(c,relabscissa(0),relabscissa(c,J[1])),2mm+0.8blue);

dot("$J_0$",J[0],2NW);
dot("$J_1$",J[1],2N);
dot("$K_0$",K[0],2W);

draw(c, 1mm+white);

đź”—geometry-fig098

Figure geometry 098 Generated with Asymptote

Show geometry/fig0980.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Arrows/Bars | #Circle | #Abscissa

import geometry;
size(6cm,0);

// currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
// show(currentcoordsys, xpen=invisible);

point A=(-1,1);
dot("$A$",A,S);

arc a=arc(circle(A,2), 45, 270);
draw(a,linewidth(3mm),ArcArrow(5mm));

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="arc(explicit arc,abscissa,abscissa)"/></asyxml>*/
draw(arc(a,angabscissa(135),angabscissa(225)),1mm+red,ArcArrow(3mm),TrueMargin(0,0.5mm));

đź”—geometry-fig100

Figure geometry 100 Generated with Asymptote

Show geometry/fig1000.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Arrows/Bars | #Circle | #Abscissa | #Coords system

import geometry;
size(6cm,0);

currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

point A=(-1,1);
point B=(2,2);
point M=(1,3);

/*<asyxml><view file="modules/geometry.asy" type="arc" signature="arccircle(point,point,point)"/></asyxml>*/
arc AMB=arccircle(A,M,B);
draw(AMB,linewidth(3mm),Arrow(5mm),TrueMargin(0,0.5mm));
dot("$C$",AMB.el.C);
draw(arccircle(A,B,M),1mm+red,Arrow(3mm));

dot("$A$",A,2SW,blue);
dot("$B$",B,2E,blue);
dot("$M$",M,2N,blue);

đź”—geometry-fig101

Figure geometry 101 Generated with Asymptote

Show geometry/fig1010.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Intersection | #Line | #Coords system

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

real R=2;

point A=(1,1);
dot("$A$", A, S, red);
point B=A+(2,1);
dot("$B$", B, N, blue);

arc a=arc(circle(A,R), -40, 180);
arc b=arc(circle(B,R), -45, 220);
line l=line(A,B);

draw(a,red);
draw(b,blue);
draw(l);

/*<asyxml><view file="modules/geometry.asy" type="point[]" signature="intersectionpoints(arc,arc)"/></asyxml>*/
point[] inter=intersectionpoints(a,b);
dot(inter);

/*<asyxml><view file="modules/geometry.asy" type="point[]" signature="intersectionpoints(line,arc)"/></asyxml>*/
point[] inter=intersectionpoints(l,a);
dot(inter);

point[] inter=intersectionpoints(l,b);
dot(inter);

đź”—geometry-fig103

Figure geometry 103 Generated with Asymptote

Show geometry/fig1030.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Arc | #Circle | #Intersection | #Line | #Coords system | #Tangent

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((1,2),i=(1,0.5),j=(-0.5,.75));
show(currentcoordsys, xpen=invisible);

real R=2;

point A=(1,1.5);
dot("$A$",A,S,red);
point B=A+(2,1);
dot("$B$",B,S,blue);

arc a=arc(circle(A,R),-40,180);
arc b=arc(circle(B,R),-45,220);

draw(a,red);
draw(b,blue);

point M=intersectionpoints(a,b)[0];
dot(M);

/*<asyxml><view file="modules/geometry.asy" type="line" signature="tangent(explicit arc,point)"/></asyxml>*/
draw(tangent(a,M), grey);
draw(tangent(b,M), grey);

/*<asyxml><view file="modules/geometry.asy" type="line" signature="tangent(explicit arc,abscissa)"/></asyxml>*/
draw(tangent(a,angabscissa(45)), grey);

đź”—geometry-fig111

Figure geometry 111 Generated with Asymptote

Show geometry/fig1110.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Triangle | #Circle | #Tangent | #Line | #Label | #Point

import geometry;
size(10cm,0);

// currentcoordsys=cartesiansystem((2,1),i=(1,0.5),j=(-0.25,0.75));
// show(currentcoordsys);

triangle t=triangle((-1,0), (2,0), (0,2));

/*<asyxml><view file="modules/geometry.asy" type="void" signature="drawline(picture,triangle,pen)"/></asyxml>*/
drawline(t, linewidth(bp));
/*<asyxml><view file="modules/geometry.asy" type="void" signature="label(picture,Label,Label,Label,triangle,real,real,pen,filltype)"/></asyxml>*/
label(t,alignFactor=4);

/*<asyxml><view file="modules/geometry.asy" type="circle" signature="circle(triangle)"/></asyxml>*/
circle cc=circle(t);
draw(cc, 0.8blue);
dot(cc.C, blue);
/*<asyxml><view file="modules/geometry.asy" type="triangle" signature="tangential(triangle)"/></asyxml>*/
triangle tgt=tangential(t);
draw(tgt, bp+0.8blue);
label("$A_1$", "$B_1$", "$C_1$", tgt, blue);

/*<asyxml><view file="modules/geometry.asy" type="circle" signature="incircle(triangle)"/></asyxml>*/
circle ic=incircle(t);
draw(ic, 0.8red);
dot(ic.C, red);
triangle intouch=intouch(t);
draw(intouch, bp+0.8red);
label("$A_2$", "$B_2$", "$C_2$", intouch, red);

/*<asyxml><view file="modules/geometry.asy" type="circle" signature="excircle(side,triangle)"/></asyxml>*/
circle ec=excircle(t.AB);
clipdraw(ec, 0.8green);
dot(ec.C, green);

ec=excircle(t.AC);
clipdraw(ec, 0.8green);
dot(ec.C, green);

ec=excircle(t.BC);
clipdraw(ec, 0.8green);
dot(ec.C, green);

/*<asyxml><view file="modules/geometry.asy" type="triangle" signature="extouch(triangle)"/></asyxml>*/
triangle ext=extouch(t);
draw(ext, bp+0.8green);
label("$A_3$", "$B_3$", "$C_3$", ext, green);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="extouch(side)"/></asyxml>*/
dot(extouch(t.AB), 0.8*green);
dot(extouch(t.BC), 0.8*green);
dot(extouch(t.CA), 0.8*green);

/*<asyxml><view file="modules/geometry.asy" type="point" signature="intouch(side)"/></asyxml>*/
dot(intouch(t.AB), 0.8*red);
dot(intouch(t.BC), 0.8*red);
dot(intouch(t.CA), 0.8*red);

// Enlarge the bounding box of the current picture
draw(box((-2.5,-3), (3.5,3.5)), invisible);

đź”—geometry-fig117

Figure geometry 117 Generated with Asymptote

Show geometry/fig1170.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Geometry.asy
Tags : #Geometry | #Inversion | #Shipout | #Bbox | #Circle | #Line

import geometry; size(15cm);

inversion inv=inversion(1,(-3.6,0));
path g1=inv*line((-1,0),(-1,1)),
g2=inv*line((1,0),(1,1));
fill(g1,0.91*yellow); draw(g1,linewidth(bp));
unfill(g2); //draw(g2,linewidth(bp));

int n=40;
for (int i=-n; i <= n; ++i) {
  path g=inv*circle((point) (0,2*i),1);
  fill(g,(1-abs(i)/n)*orange);
  // draw(g,bp+0.8*orange); //draw(g,black);
}
shipout(bbox(5mm,Fill(rgb(0.95,0.95,0.7))));

This page was generated by the Asymptote Exemples Builder
Last modified the 2025-06-30 22:08:01
©2011 Philippe Ivaldi

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