Question 96
$AC$ is hypotenuse of right triangle $ABC$, $BH$ is its altitude. Points $M$ and $N$ are the midpoints of segments $AH$ and $CH$ correspondingly. Lines $BM$ and $BN$ intersect for second time the circumscribed circle of triangle $ABC$ in points $P$ and $Q$ correspondingly. Segments $AQ$ and $CP$ intersect in point $R$. Prove that line $BR$ passes through the midpoint of segment $MN$.