---
id: 5900f46e1000cf542c50ff80
title: 'Problem 257: Angular Bisectors'
challengeType: 5
forumTopicId: 301905
dashedName: 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?

# --hints--

`euler257()` should return 139012411.

```js
assert.strictEqual(euler257(), 139012411);
```

# --seed--

## --seed-contents--

```js
function euler257() {

  return true;
}

euler257();
```

# --solutions--

```js
// solution required
```