freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-264-triangle-centres.md

---
id: 5900f4751000cf542c50ff87
challengeType: 5
title: 'Problem 264: Triangle Centres'
forumTopicId: 301913
---

## Description
<section id='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.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler264()</code> should return 2816417.1055.
    testString: assert.strictEqual(euler264(), 2816417.1055);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler264() {

  return true;
}

euler264();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>