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INMO 2000 Problem 4

  • Answer

In a convex quadrilateral PQRS,PQ=RS,(3+1)QR=SPP Q R S, P Q=R S,(\sqrt{3}+1) Q R=S P and ∠RSP−∠SPQ=\angle R S P-\angle S P Q= 30∘30^{\circ}. Prove that

∠PQR−∠QRS=90∘\angle P Q R-\angle Q R S=90^{\circ}

Dataset text NuminaMath olympiads. Quoted with source.

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\angle P Q R-\angle Q R S=\frac{\pi}{2}

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