47 lines
1.0 KiB
Markdown
47 lines
1.0 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.
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(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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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 area(ABC)/area(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 area(ABC)/area(AEG) is integral?
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# --hints--
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`euler257()` should return 139012411.
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```js
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assert.strictEqual(euler257(), 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 euler257() {
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return true;
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}
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euler257();
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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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