ILL 1986 Problem 79

Let $AA_1,BB_1, CC_1$ be the altitudes in an acute-angled triangle $ABC$ , $K$ and $M$ are points on the line segments $A_1C_1$ and $B_1C_1$ respectively. Prove that if the angles $MAK$ and $CAA_1$ are equal, then the angle $C_1KM$ is bisected by $AK.$