1988 OIM Problems/Problem 4

Problem

Let $ABC$ be a triangle which sides are $a$ , $b$ , $c$ . We divide each side of the triangle in $n$ equal segments. Let $S$ 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.

Page

Toolbox

Search

1988 OIM Problems/Problem 4

Problem

Solution