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One on quads

Source: INMO 2000 Problem 4

October 10, 2005
trigonometrygeometryPythagorean Theoremgeometry unsolved

Problem Statement

In a convex quadrilateral PQRSPQRS, PQ=RSPQ =RS, (3+1)QR=SP(\sqrt{3} +1 )QR = SP and ∠RSP−∠SQP=30∘\angle RSP - \angle SQP = 30^{\circ}. Prove that ∠PQR−∠QRS=90∘.\angle PQR - \angle QRS = 90^{\circ}.
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