MathDB
Parallel lines in pentagon

Source: JBMO 2009 Problem 1

June 27, 2009
geometrytrapezoidgeometry proposedpentagon

Problem Statement

Let ABCDE ABCDE be a convex pentagon such that AB\plus{}CD\equal{}BC\plus{}DE and k k a circle with center on side AE AE that touches the sides AB AB, BC BC, CD CD and DE DE at points P P, Q Q, R R and S S (different from vertices of the pentagon) respectively. Prove that lines PS PS and AE AE are parallel.
Back to ProblemsView on AoPS