72 lines
1.5 KiB
Markdown
72 lines
1.5 KiB
Markdown
---
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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 $\text{perimeter} ≤ 50$.
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Listed and shown in ascending order of their perimeter, they are:
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<table>
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<tbody>
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<tr>
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<td>
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A(-4, 3), B(5, 0), C(4, -3)<br>
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A(4, 3), B(5, 0), C(-4, -3)<br>
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A(-3, 4), B(5, 0), C(3, -4)<br>
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<br><br>
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A(3, 4), B(5, 0), C(-3, -4)<br>
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A(0, 5), B(5, 0), C(0, -5)<br>
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A(1, 8), B(8, -1), C(-4, -7)<br>
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<br><br>
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A(8, 1), B(1, -8), C(-4, 7)<br>
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A(2, 9), B(9, -2), C(-6, -7)<br>
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A(9, 2), B(2, -9), C(-6, 7)<br>
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</td>
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<td><img class="img-responsive center-block" alt="nine triangles ABC with perimeter ≤ 50" src="https://cdn.freecodecamp.org/curriculum/project-euler/triangle-centres.gif" style="background-color: white; padding: 10px;"></td>
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</tr>
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</tbody>
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</table>
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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 $\text{perimeter} ≤ {10}^5$. Enter as your answer the sum of their perimeters rounded to four decimal places.
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# --hints--
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`triangleCentres()` should return `2816417.1055`.
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```js
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assert.strictEqual(triangleCentres(), 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 triangleCentres() {
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return true;
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}
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triangleCentres();
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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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