56 lines
1.6 KiB
Markdown
56 lines
1.6 KiB
Markdown
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---
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id: 5900f3fc1000cf542c50ff0e
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challengeType: 5
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title: 'Problem 143: Investigating the Torricelli point of a triangle'
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videoUrl: ''
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localeTitle: 问题143：研究三角形的Torricelli点
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---
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## Description
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<section id="description">设ABC为三角形，所有内角均小于120度。设X为三角形内的任意点，并使XA = p，XC = q，XB = r。 Fermat挑战Torricelli找到X的位置，使p + q + r最小化。 Torricelli能够证明，如果在三角形ABC的每一侧构造等边三角形AOB，BNC和AMC，则AOB，BNC和AMC的外接圆将在三角形内的单个点T处相交。此外，他证明了T，称为Torricelli / Fermat点，最小化p + q + r。更值得注意的是，可以证明，当总和最小化时，AN = BM = CO = p + q + r，并且AN，BM和CO也在T处相交。 <p>如果总和最小化并且a，b，c，p，q和r都是正整数，我们将称三角形ABC为Torricelli三角形。例如，a = 399，b = 455，c = 511是Torricelli三角形的示例，其中p + q + r = 784.找到Torricelli三角形的p + q +r≤120000的所有不同值的总和。 </p></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>euler143()</code>应返回30758397。
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testString: 'assert.strictEqual(euler143(), 30758397, "<code>euler143()</code> should return 30758397.");'
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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 euler143() {
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// Good luck!
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return true;
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}
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euler143();
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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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