OME 2005 Problem 3

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 $ABC \dots XYZ$ is a regular polygon with $n$ sides of length $1$ . The $n-3$ diagonals that go out from vertex $A$ divide the triangle $ZAB$ in $n-2$ smaller triangles. Prove that each one of these triangles is multiplicative.