A point is chosen inside a regular k-gon in such a way that its orthogonal projections on to the sides all meet the respective sides at interior points. These points divide the sides into 2k segments. Let these segments be enumerated consecutively by the numbers 1,2,3,...,2k. Prove that the sum of the lengths of the segments having even numbers equals the sum of the segments having odd numbers.(A Andjans, Riga) combinatorial geometrycombinatoricscumprojectionregular polygon