MathDB

8

Part of 2010 Canadian Mathematical Olympiad Qualification Repechage

Problems(1)

3 Layered Parallolegrams

Source: Canadian Repêchage 2010: Problem 8

5/6/2014
Consider three parallelograms P1, P2, P3P_1,~P_2,~ P_3. Parallelogram P3P_3 is inside parallelogram P2P_2, and the vertices of P3P_3 are on the edges of P2P_2. Parallelogram P2P_2 is inside parallelogram P1P_1, and the vertices of P2P_2 are on the edges of P1P_1. The sides of P3P_3 are parallel to the sides of P1P_1. Prove that one side of P3P_3 has length at least half the length of the parallel side of P1P_1.
geometryparallelogramgeometry proposed