IMO 2009 Shortlist G3

Let ABC be a triangle. The incircle of ABC touches the sides AB and AC at the points Z and Y , respectively. Let G be th...

IMO 2009 Shortlist G3

Category: Geometry

Problem

Let ABC be a triangle. The incircle of ABC touches the sides AB and AC at the points Z and Y , respectively. Let G be the point where the lines BY and CZ meet, and let R and S be points such that the two quadrilaterals BCY R and BCSZ are parallelograms. Prove that GR = GS.