---
id: 5900f4941000cf542c50ffa7
title: 'Problem 296: Angular Bisector and Tangent'
challengeType: 1
forumTopicId: 301948
dashedName: problem-296-angular-bisector-and-tangent
---

# --description--

Given is an integer sided triangle $ABC$ with $BC ≤ AC ≤ AB$. $k$ is the angular bisector of angle $ACB$. $m$ is the tangent at $C$ to the circumscribed circle of $ABC$. $n$ is a line parallel to $m$ through $B$.

The intersection of $n$ and $k$ is called $E$.

<img alt="triangle ABC, with k - the angular bisector of angle ACB, m - tangent at point C, n - line parallel to m through B, and point E - intersection of k and n" src="https://cdn.freecodecamp.org/curriculum/project-euler/angular-bisector-and-tangent.gif" style="background-color: white; padding: 10px; display: block; margin-right: auto; margin-left: auto; margin-bottom: 1.2rem;">

How many triangles $ABC$ with a perimeter not exceeding $100\\,000$ exist such that $BE$ has integral length?

# --hints--

`angularBisectorAndTangent()` should return `1137208419`.

```js
assert.strictEqual(angularBisectorAndTangent(), 1137208419);
```

# --seed--

## --seed-contents--

```js
function angularBisectorAndTangent() {

  return true;
}

angularBisectorAndTangent();
```

# --solutions--

```js
// solution required
```
