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id	challengeType	title	forumTopicId
5900f46e1000cf542c50ff80	5	Problem 257: Angular Bisectors	301905

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?

Instructions

Tests

tests:
  - text: <code>euler257()</code> should return 139012411.
    testString: assert.strictEqual(euler257(), 139012411);

Challenge Seed

function euler257() {
  // Good luck!
  return true;
}

euler257();

Solution

// solution required

1.2 KiB Raw Blame History