SILK-ROAD 2014 Problem 2

Let $w$ be the circumcircle of non-isosceles acute triangle $ABC$ . Tangent lines to $w$ in $A$ and $B$ intersect at point $S$ . Let M be the midpoint of $AB$ , and $H$ be the orthocenter of triangle $ABC$ . The line $HA$ intersects lines $CM$ and $CS$ at points $M_a$ and $S_a$ , respectively. The points $M_b$ and $S_b$ are defined analogously. Prove that $M_aS_b$ and $M_bS_a$ are the altitudes of triangle $M_aM_bH$ .