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

## Description
<section id='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?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler257()</code> should return 139012411.
    testString: assert.strictEqual(euler257(), 139012411);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler257() {
  // Good luck!
  return true;
}

euler257();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>