Circumcenter and orthocenter

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Let acute-angled triangle $ABC$ is inscribed in a circle $k(O)$. Heights through $A, B, C$ intersects $k$ at the points $H_A, H_B, H_C$ respectively. $A_1$ is the intersection point of $OH_A$ and $BC$, $B_1$ is the intersection point of $OH_B$ and $CA$, $C_1$ is the intersection point of $OH_C$ and $AB$. Prove that $AA_1$, $BB_1$, $CC_1$ intersects at a common point.