Heights and equal angles 1

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In the acute-angled triangle $ABC$ with orthocenter $H$ $A_1, B_1, C_1$ are feets of the altitudes from the vertices $A, B, C$ respectively. $P$ is a random internal point on the segment $CH$. $AP$ and $BP$ intersects $BB_1$ and $AA_1$ at the points $M$ and $N$ respectively. Prove that $\angle CC_1M = \angle CC_1N$.