Question 57
Let $O$ be an interior point of an acute-angled $\triangle ABC$. Denote by $A_1$, $B_1$ and $C_1$ its projection on the sides $BC$, $AC$ and $AB$. Let $P$ be the intersecting point of the lines through $A$ and $B$, orthogonal to $B_1C_1$ and $A_1C_1$, respectively. If $H$ is the projection of $P$ on $AB$, prove that the points $A_1$, $B_1$, $C_1$ and $H$ are con-cyclic.
