# Asymptote: Useful functions

## Labeling angles

The bundled `markers`

package provides a useful function for marking angles. The exact same function exists in the `geometry`

package.

void

markangle(picturepic=currentpicture,

LabelL="", intn=1, realradius=0, realspace=0,

linel1, linel2,

arrowbararrow=None, penp=currentpen,

marginmargin=NoMargin, markermarker=nomarker)

As with other angle functions, you can replace `line l1, line l2`

with `pair A, pair O, pair B`

, which would mark the angle . The function will draw an arc from line AO or l1 to line BO or l2, counterclockwise, with radius and label it with the provided `Label L`

.

If the function draws the angle in the wrong direction, try swapping the first pair with the third pair, or, if you put in lines, swapping l1 and l2.

Here's an example to do that with an orange pen:

```
pair A = (1,1);
pair O = (0,0);
pair B = (2,0);
draw(O--A);
draw(O--B);
import geometry;
markangle("$45^o$", B, O, A, p=orange);
```

### Olympiad

*Main article: Asymptote: Marking Angles*

The `olympiad`

package provides a function that generates a path that can then be drawn using the draw() function.

path

anglemark(pairA, pairB, pairC,

realt=8, ... real[]s=8)

*t* is the radius of the first line, and s[] stores the radius of subsequent lines.
To label it, simply use the label() function per usual.

```
pair A = (1,1);
pair O = (0,0);
pair B = (2,0);
draw(O--A);
draw(O--B);
import olympiad;
draw(anglemark(B, O, A), p=orange);
label("$45^\circ$", anglemark(B, O, A), NE);
```

As you can see, this is an inferior method as the path also covers part of the angle and the origin of labeling is the point instead of the angle mark. However, anglemark() makes a bit more abstract sense and is more flexible.

## 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[0],3bp+blue);
dot(x[1],3bp+blue);
draw(x[0] -- x[1],1bp+red);
```

```
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[0]--x[1]--x[2]--x[3]--x[4]--x[5]--cycle,black);
dot((0,0),white);
```

Note that this function will cause an error if the paths involved do not intersect.