---
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 (r/4,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°&lt;α&lt;180°.

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

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

# --hints--

`euler210()` should return 1598174770174689500.

```js
assert.strictEqual(euler210(), 1598174770174689500);
```

# --seed--

## --seed-contents--

```js
function euler210() {

  return true;
}

euler210();
```

# --solutions--

```js
// solution required
```
