Let $ABC$ be a right-angled triangle with hypotenuse $AB$. Denote by $D$ the foot of the altitude from $C$. Let $Q, R$, and $P$ be the midpoints of the segments $AD, BD$, and $CD$, respectively. Prove that $\angle AP B + \angle QCR = 180^o$. Czech Republic
Problem
Source: Czech-Polish-Slovak Junior Match 2016, team p1 CPSJ
Tags: geometry, midpoints, angles, Angle Chasing