Project Euler #143: Investigating the Torricelli point of a triangle

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    Difficulty "Easy"? Seriously? That's deliberate misinformation.

    It's HARD. The gyst of the problem is to find triangles where:

    a. all sides are integer numbers, and

    b. all 3 distances from the angles to the Torricelli point is also whole numbers (not fractional numbers).

    For that you need to apply Law of cosines to 120-degree triangles, that would give you equasions like that:

    c^2 = p^2+r^2 + pr

    Considering p, r, and c are integer numbers, you need to build a collection of pairs (p, r) where p^2+r^2 + pr would give you a square number.

    Building this collection is not trivial, here's a useful article on that: http://www.geocities.ws/fredlb37/node9.html