1.0 KiB
1.0 KiB
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