Question 168
The point $P$ lies inside triangle $ABC$. Denote by $O_A, O_B, O_C$ the circumcenters of triangles $PBC, PAC, PAB$ respectively. Let $O_P$ be the circumcenter of triangle $O_A O_B O_C$. Prove that the point $P$ satisfies the condition $O_P = P$ if $P$ is the orthocenter of triangle $ABC$.