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Perpendicular Likers Go on

Source: Rioplatense L3 2023 #2

December 6, 2023
geometry

Problem Statement

Let ABCDABCD be a convex quadrilateral with AB>ADAB>AD and ∠B=∠D=90∘\angle B=\angle D=90^{\circ}. Let PP be a point in the side ABAB such that AP=ADAP=AD. The lines PDPD and BCBC cut in the point QQ. The perpendicular line to ACAC passing by QQ cuts ABAB in the point RR. Let SS be the foot of perpendicular of DD to the line ACAC. Prove that ∠PSQ=∠RCP\angle PSQ=\angle RCP.
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