MathDB
First problem

Source: Cono sur 2018

August 26, 2018
geometrycono sur

Problem Statement

Let ABCDABCD be a convex quadrilateral, where RR and SS are points in DCDC and ABAB, respectively, such that AD=RCAD=RC and BC=SABC=SA. Let PP, QQ and MM be the midpoints of RDRD, BSBS and CACA, respectively. If ∠MPC+∠MQA=90\angle MPC + \angle MQA = 90, prove that ABCDABCD is cyclic.
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