47 lines
1.4 KiB
Markdown
47 lines
1.4 KiB
Markdown
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---
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id: 5900f46e1000cf542c50ff80
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title: 'Problem 257: Angular Bisectors'
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challengeType: 5
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forumTopicId: 301905
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dashedName: problem-257-angular-bisectors
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---
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# --description--
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Given is an integer sided triangle $ABC$ with sides $a ≤ b ≤ c$. ($AB = c$, $BC = a$ and $AC = b$).
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The angular bisectors of the triangle intersect the sides at points $E$, $F$ and $G$ (see picture below).
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<img class="img-responsive center-block" alt="triangle ABC, with angular bisectors intersecting sides at the points E, F and G" src="https://cdn.freecodecamp.org/curriculum/project-euler/angular-bisectors.gif" style="background-color: white; padding: 10px;" />
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The segments $EF$, $EG$ and $FG$ partition the triangle $ABC$ into four smaller triangles: $AEG$, $BFE$, $CGF$ and $EFG$. It can be proven that for each of these four triangles the ratio $\frac{\text{area}(ABC)}{\text{area}(\text{subtriangle})}$ is rational. However, there exist triangles for which some or all of these ratios are integral.
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How many triangles $ABC$ with perimeter $≤ 100\\,000\\,000$ exist so that the ratio $\frac{\text{area}(ABC)}{\text{area}(AEG)}$ is integral?
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# --hints--
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`angularBisectors()` should return `139012411`.
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```js
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assert.strictEqual(angularBisectors(), 139012411);
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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 angularBisectors() {
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return true;
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}
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angularBisectors();
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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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