Question 26
Let $C_0,B_0$ be the midpoints of $AB,AC$ in a non-isosceles acute triangle $ABC$. Let $O,H$ be its circumcenter and orthocenter. Lines $BH,OC_0$ meet at $P$, and lines $CH,OB_0$ meet at $Q$. If $OPHQ$ is a rhombus, prove that $A,P,Q$ are collinear.