KöMaL 2016 B4790

In a scalene triangle $ABC$ , a Thales circle is drawn over each median. The Thales circles of the medians drawn from vertices $A$ , $B$ and $C$ intersect the circumscribed circle of the triangle $ABC$ again at points $A_1$, $B_1$, and $C_1$, respectively. Prove that the perpendiculars drawn to $AA_1$ at $A$ , to $BB_1$ at $B$ and to $CC_1$ at $C$ are concurrent.