Two circles intersect at points $A$ and $B$. The line $\ell$ through A intersects the circles at $C$ and $D$, respectively. Let $M, N$ be the midpoints of arc $BC$ and arc $BD$. which does not contain $A$, and suppose that $K$ is the midpoint of the segment $CD$ . Prove that $\angle MKN=90^o$.
Problem
Source: Indonesia INAMO Shortlist 2009 G5 https://artofproblemsolving.com/community/c1101409_
Tags: geometry, circles, right angle