Heights, middles and a circle

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Let $AA_1, BB_1, CC_1$ are the heights of the triangle $ABC$. $M, N, P$ are the middles of the $AA_1, BB_1, CC_1$, respectively. $M_1$ and $M_2$ are the feets of the perpendiculars from $M_1$ to $AB$ and $BC$ respectively. $N_1$ and $N_2$ are the feets of the perpendiculars from $N$ to the sides $CB$ and $BA$ respectively. $P_1$ and $P_2$ are the feets of the perpendiculars from $P$ to the sides $AB$ and $BC$ respectively. Prove that $M_1, M_2, N_1, N_2, P_1, P_2$ are concyclic.