---
id: 5900f43e1000cf542c50ff50
title: 'Problem 210: Obtuse Angled Triangles'
challengeType: 5
forumTopicId: 301852
dashedName: problem-210-obtuse-angled-triangles
---

# --description--

Consider the set $S(r)$ of points ($x$,$y$) with integer coordinates satisfying $|x| + |y| ≤ r$.

Let $O$ be the point (0,0) and $C$ the point ($\frac{r}{4}$,$\frac{r}{4}$).

Let $N(r)$ be the number of points $B$ in $S(r)$, so that the triangle $OBC$ has an obtuse angle, i.e. the largest angle $α$ satisfies $90°<α<180°$.

So, for example, $N(4)=24$ and $N(8)=100$.

What is $N(1\\,000\\,000\\,000)$?

# --hints--

`obtuseAngledTriangles()` should return `1598174770174689500`.

```js
assert.strictEqual(obtuseAngledTriangles(), 1598174770174689500);
```

# --seed--

## --seed-contents--

```js
function obtuseAngledTriangles() {

  return true;
}

obtuseAngledTriangles();
```

# --solutions--

```js
// solution required
```