---
id: 5900f4751000cf542c50ff87
title: 'Problem 264: Triangle Centres'
challengeType: 5
forumTopicId: 301913
dashedName: problem-264-triangle-centres
---

# --description--

Consider all the triangles having:

All their vertices on lattice points.

Circumcentre at the origin O.

Orthocentre at the point H(5, 0).

There are nine such triangles having a perimeter ≤ 50.

Listed and shown in ascending order of their perimeter, they are:

A(-4, 3), B(5, 0), C(4, -3) A(4, 3), B(5, 0), C(-4, -3) A(-3, 4), B(5, 0), C(3, -4) A(3, 4), B(5, 0), C(-3, -4) A(0, 5), B(5, 0), C(0, -5) A(1, 8), B(8, -1), C(-4, -7) A(8, 1), B(1, -8), C(-4, 7) A(2, 9), B(9, -2), C(-6, -7) A(9, 2), B(2, -9), C(-6, 7)

The sum of their perimeters, rounded to four decimal places, is 291.0089.

Find all such triangles with a perimeter ≤ 105. Enter as your answer the sum of their perimeters rounded to four decimal places.

# --hints--

`euler264()` should return 2816417.1055.

```js
assert.strictEqual(euler264(), 2816417.1055);
```

# --seed--

## --seed-contents--

```js
function euler264() {

  return true;
}

euler264();
```

# --solutions--

```js
// solution required
```