Problem

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Tags: geometry



Let $H$ be orthocenter of an acute $\Delta ABC$, $M$ is a midpoint of $AC$. Line $MH$ meets lines $AB, BC$ at points $A_1, C_1$ respectively, $A_2$ and $C_2$ are projections of $A_1, C_1$ onto line $BH$ respectively. Prove that lines $CA_2, AC_2$ meet at circumscribed circle of $\Delta ABC$. Proposed by Anton Trygub