55 lines
1.1 KiB
Markdown
55 lines
1.1 KiB
Markdown
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---
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id: 5900f4751000cf542c50ff87
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title: 'Problem 264: Triangle Centres'
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challengeType: 5
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forumTopicId: 301913
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dashedName: problem-264-triangle-centres
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---
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# --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) 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)
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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. Enter as your answer the sum of their perimeters rounded to four decimal places.
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# --hints--
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`euler264()` should return 2816417.1055.
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```js
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assert.strictEqual(euler264(), 2816417.1055);
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```
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# --seed--
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## --seed-contents--
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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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# --solutions--
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```js
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// solution required
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```
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