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A rhombus' vertices on another rhombus' boundary

Source: INAMO 2002 - Problem 7

August 5, 2011
geometryrhombusgeometry unsolved

Problem Statement

Let ABCDABCD be a rhombus where ∠DAB=60∘\angle DAB = 60^\circ, and PP be the intersection between ACAC and BDBD. Let Q,R,SQ,R,S be three points on the boundary of ABCDABCD such that PQRSPQRS is a rhombus. Prove that exactly one of Q,R,SQ,R,S lies on one of A,B,C,DA,B,C,D.
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