寻找两个圆的交点

Question

我正在尝试使用 pair[] Intersectionpoints 来查找并标记由路径 h 和路径 g 定义的圆的交点。谢谢您的帮助。

\documentclass{standalone}
\usepackage{asypictureB}

\begin{document}

\begin{asypicture}{name=Label}
import olympiad;
size(7cm);
import graph;
pair A=(0,0);
dot(A);
label("$A$",A,W);
pair C=A+18dir(40);
dot(C);
label("$C$",C,N);
pair D=A+16dir(20);
dot(D);
label("$D$",D,SE);
pair e=A+9dir(20);
dot(e);
label("$E$",e,NE);
pair F=A+8dir(40);
dot(F);
label("$F$",F,W);
path g = circle(A,12);
draw(g);
path h = circumcircle(F,D,C);
pair[] intersectionpoints(path g, path h);
dot(point([0]);
dot(point([1]);
draw(A--C);
draw(A--D);
pair O=circumcenter(F,D,C); // olympiad - circumcenter
dot(O);
label("$O$",O,S);
draw(circumcircle(F,D,C)); // olympiad - circumcircle
\end{asypicture}

\end{document}

Answer 1

下载opympiad.asy后本网站，这很容易。我猜你误解了这句话这个很好的教程所以我做了pair[] intersectionpoints(path g, path h);一些调整，并删除了其他语法错误，以获得

\documentclass{standalone}
\usepackage{asypictureB}

\begin{document}

\begin{asypicture}{name=Label}
import olympiad;
size(7cm);
import graph;
pair A=(0,0);
dot(A);
label("$A$",A,W);
pair C=A+18*dir(40);
dot(C);
label("$C$",C,N);
pair D=A+16*dir(20);
dot(D);
label("$D$",D,SE);
pair e=A+9*dir(20);
dot(e);
label("$E$",e,NE);
pair F=A+8*dir(40);
dot(F);
label("$F$",F,W);
path g = circle(A,12);
draw(g);
path h = circumcircle(F,D,C);
pair[] ipoints = intersectionpoints(g,h);
dot(ipoints[0]);
dot(ipoints[1]);
draw(A--C);
draw(A--D);
pair O=circumcenter(F,D,C); // olympiad - circumcenter
dot(O);
label("$O$",O,S);
draw(h); // olympiad - circumcircle
\end{asypicture}
\end{document}

Answer 2

只需提及geometry.asy（包含在 Asymptote 中）提供了大量平面几何例程（三角形、圆形、椭圆形等）和适当的结构。例如，如果C是圆形，C.C则为中心，而C.r为半径。这里是带有软件包的 marmot 答案的复制/粘贴geometry.asy。

    import geometry;
    point A=(0,0);
    dot(A);
    label("$A$",A,W);
    point C=A+18*dir(40);
    dot(C);
    label("$C$",C,N);
    point D=A+16*dir(20);
    dot(D);
    label("$D$",D,SE);
    point e=A+9*dir(20);
    dot(e);
    label("$E$",e,NE);
    point F=A+8*dir(40);
    dot(F);
    label("$F$",F,W);
    circle g = circle(A,12);
    draw(g);
    circle h = circle(F,D,C);
    pair[] ipoints = intersectionpoints(g,h);
    dot(ipoints[0]);
    dot(ipoints[1]);
    draw(A--C);
    draw(A--D);
    point O=h.C; // circle is a structure, h.C the center, h.r the radius
    label("$r\approx$"+string(h.r,4),(18,1));
    dot(O);
    label("$O$",O,S);
    draw(h); 

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