---
id: 5900f4e11000cf542c50fff4
title: 'Problem 373: Circumscribed Circles'
challengeType: 5
forumTopicId: 302035
dashedName: problem-373-circumscribed-circles
---

# --description--

Every triangle has a circumscribed circle that goes through the three vertices. Consider all integer sided triangles for which the radius of the circumscribed circle is integral as well.

Let $S(n)$ be the sum of the radii of the circumscribed circles of all such triangles for which the radius does not exceed $n$.

$S(100) = 4\\,950$ and $S(1\\,200) = 1\\,653\\,605$.

Find $S({10}^7)$.

# --hints--

`circumscribedCircles()` should return `727227472448913`.

```js
assert.strictEqual(circumscribedCircles(), 727227472448913);
```

# --seed--

## --seed-contents--

```js
function circumscribedCircles() {

  return true;
}

circumscribedCircles();
```

# --solutions--

```js
// solution required
```