45 lines
1.2 KiB
Markdown
45 lines
1.2 KiB
Markdown
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---
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id: 5900f4941000cf542c50ffa7
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title: 'Problem 296: Angular Bisector and Tangent'
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challengeType: 5
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forumTopicId: 301948
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dashedName: problem-296-angular-bisector-and-tangent
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---
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# --description--
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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 $B$.
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The intersection of $n$ and $k$ is called $E$.
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<img class="img-responsive center-block" 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;" />
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How many triangles $ABC$ with a perimeter not exceeding $100\\,000$ exist such that $BE$ has integral length?
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# --hints--
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`angularBisectorAndTangent()` should return `1137208419`.
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```js
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assert.strictEqual(angularBisectorAndTangent(), 1137208419);
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```
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# --seed--
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## --seed-contents--
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```js
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function angularBisectorAndTangent() {
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return true;
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}
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angularBisectorAndTangent();
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```
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# --solutions--
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```js
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// solution required
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```
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