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angle chasing candidate, <AP B + < QCR = 180^o , 3 midpoints related

Source: Czech-Polish-Slovak Junior Match 2016, team p1 CPSJ

January 20, 2020
geometrymidpointsanglesAngle Chasing

Problem Statement

Let ABCABC be a right-angled triangle with hypotenuse ABAB. Denote by DD the foot of the altitude from CC. Let Q,RQ, R, and PP be the midpoints of the segments AD,BDAD, BD, and CDCD, respectively. Prove that ∠APB+∠QCR=180o\angle AP B + \angle QCR = 180^o.
Czech Republic
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