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id	title	challengeType	forumTopicId	dashedName
5900f46e1000cf542c50ff80	Problem 257: Angular Bisectors	5	301905	problem-257-angular-bisectors

--description--

Given is an integer sided triangle ABC with sides a ≤ b ≤ c.

(AB = c, BC = a and AC = b).

The angular bisectors of the triangle intersect the sides at points E, F and G (see picture below).

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.

How many triangles ABC with perimeter≤100,000,000 exist so that the ratio area(ABC)/area(AEG) is integral?

--hints--

euler257() should return 139012411.

assert.strictEqual(euler257(), 139012411);

--seed--

--seed-contents--

function euler257() {

  return true;
}

euler257();

--solutions--

// solution required

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