78 lines
1.3 KiB
Markdown
78 lines
1.3 KiB
Markdown
---
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id: 5900f4751000cf542c50ff87
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challengeType: 5
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title: 'Problem 264: Triangle Centres'
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forumTopicId: 301913
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---
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## Description
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<section id='description'>
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Consider all the triangles having:
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All their vertices on lattice points.
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Circumcentre at the origin O.
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Orthocentre at the point H(5, 0).
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There are nine such triangles having a perimeter ≤ 50.
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Listed and shown in ascending order of their perimeter, they are:
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A(-4, 3), B(5, 0), C(4, -3)
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A(4, 3), B(5, 0), C(-4, -3)
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A(-3, 4), B(5, 0), C(3, -4)
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A(3, 4), B(5, 0), C(-3, -4)
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A(0, 5), B(5, 0), C(0, -5)
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A(1, 8), B(8, -1), C(-4, -7)
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A(8, 1), B(1, -8), C(-4, 7)
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A(2, 9), B(9, -2), C(-6, -7)
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A(9, 2), B(2, -9), C(-6, 7)
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The sum of their perimeters, rounded to four decimal places, is 291.0089.
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Find all such triangles with a perimeter ≤ 105.
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Enter as your answer the sum of their perimeters rounded to four decimal places.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler264()</code> should return 2816417.1055.
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testString: assert.strictEqual(euler264(), 2816417.1055);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler264() {
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return true;
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}
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euler264();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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