# Asymptote: Useful functions

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## Intersection points

pair[] intersectionpoints(path, path);

Examples:

```size(8cm,0);
import math;
import graph;
real r,s;
pair a,b, common;
path circ1, circ2;
r=1; s=1;
a=(0,0);
b=(1,0);
circ1=circle(a,r);
circ2=circle(b,s);
draw(circ1,linewidth(1bp));
draw(circ2,1bp+green);
pair [] x=intersectionpoints(circ1, circ2);
dot(x,3bp+blue);
dot(x,3bp+blue);
draw(x -- x,1bp+red);``` $[asy]size(200,200); import math; import graph; real r,s; pair a,b, common; path circ1, circ2; r=1; s=1; a=(0,0); b=(1,0); circ1=circle(a,r); circ2=circle(b,s); draw(circ1,linewidth(1bp)); draw(circ2,1bp+green); pair [] x=intersectionpoints(circ1, circ2); dot(x,3bp+blue); dot(x,3bp+blue); draw(x -- x,1bp+red);[/asy]$

```path g=(-3,-sqrt(3))--(3,-sqrt(3))--(0,2*sqrt(3))--cycle;
draw(g,black);
path p=-2/3*(-3,-sqrt(3))--(-2/3)*(3,-sqrt(3))--(-2/3)*(0,2*sqrt(3))--cycle;
draw(p,black);
pair [] x=intersectionpoints(g, p);
fill(x--x--x--x--x--x--cycle,black);
dot((0,0),white);
``` $[asy] path g=(-3,-sqrt(3))--(3,-sqrt(3))--(0,2*sqrt(3))--cycle; draw(g,black); path p=-2/3*(-3,-sqrt(3))--(-2/3)*(3,-sqrt(3))--(-2/3)*(0,2*sqrt(3))--cycle; draw(p,black); pair [] x=intersectionpoints(g, p); fill(x--x--x--x--x--x--cycle,black); dot((0,0),white); [/asy]$ Note that this function will cause an error if the paths involved do not intersect.