1988 OIM Problems/Problem 4
Problem
Let 
be a triangle which sides are 
, 
, 
. We divide each side of the triangle in 
equal segments. Let 
be the sum of the squares of the distances from each vertex to each of the points dividing the opposite side different from the vertices.
Prove that $\frac{S}{a^2+b^2+c^2} is rational.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
