---
id: 5900f4311000cf542c50ff43
title: 'Problem 195: Inscribed circles of triangles with one angle of 60 degrees'
challengeType: 5
forumTopicId: 301833
dashedName: problem-195-inscribed-circles-of-triangles-with-one-angle-of-60-degrees
---

# --description--

Let's call an integer sided triangle with exactly one angle of 60° a 60° triangle.

Let $r$ be the radius of the inscribed circle of such a 60° triangle.

There are 1234 60° triangles for which $r ≤ 100$.

Let $T(n)$ be the number of 60° triangles for which $r ≤ n$, so $T(100) = 1234$, $T(1000) = 22767$, and $T(10000) = 359912$.

Find $T(1053779)$.

# --hints--

`inscribedCirclesOfTriangles()` should return `75085391`.

```js
assert.strictEqual(inscribedCirclesOfTriangles(), 75085391);
```

# --seed--

## --seed-contents--

```js
function inscribedCirclesOfTriangles() {

  return true;
}

inscribedCirclesOfTriangles();
```

# --solutions--

```js
// solution required
```