---
id: 5900f46e1000cf542c50ff80
challengeType: 5
title: 'Problem 257: Angular Bisectors'
---
## Description
Given is an integer sided triangle ABC with sides a ≤ b ≤ c.
(AB = c, BC = a and AC = b).
The angular bisectors of the triangle intersect the sides at points E, F and G (see picture below).
The segments EF, EG and FG partition the triangle ABC into four smaller triangles: AEG, BFE, CGF and EFG.
It can be proven that for each of these four triangles the ratio area(ABC)/area(subtriangle) is rational.
However, there exist triangles for which some or all of these ratios are integral.
How many triangles ABC with perimeter≤100,000,000 exist so that the ratio area(ABC)/area(AEG) is integral?
## Instructions
## Tests
```yml
tests:
- text: euler257() should return 139012411.
testString: assert.strictEqual(euler257(), 139012411, 'euler257() should return 139012411.');
```
## Challenge Seed
```js
function euler257() {
// Good luck!
return true;
}
euler257();
```