RO-TST 2010 Problem 15

Let $ABC$ be a scalene triangle. The tangents at the perpendicular foot dropped from $A$ on the line $BC$ and the midpoint of the side $BC$ to the nine-point circle meet at the point $A'$ ,; the points $B'$ and $C'$ are defined similarly. Prove that the lines $AA'$ , $BB'$ and $CC'$ are concurrent.

Gazeta Matematica