Spanish Mathematical Olympiad 2005, Problem 3
Source: 2005 Spanish Mathematical Olympiad
July 17, 2017
geometry
Problem Statement
We will say that a triangle is multiplicative if the product of the heights of two of its sides is equal to the length of the third side. Given is a regular polygon with sides of length . The diagonals that go out from vertex divide the triangle in smaller triangles. Prove that each one of these triangles is multiplicative.