VTMO 2026 - Grade 7 - Semifinal - SET 9 - Self-study Question 5

Let $P$ be inside the right angle $xOy$. Take $A$ on ray $Ox$ and $B$ on ray $Oy$ such that $\angle APB=90^\circ$. On the rays opposite to $AP$ and $BP$, take $C,D$ respectively so that $CA=OA$ and $BD=OB$.

a) Prove that $C,O,D$ are collinear.

b) Let $M$ be the midpoint of $CD$. Prove that $\angle AMB=90^\circ$.