MathNet 2012 Question 23

Let $ABC$ be a triangle. Point $D$ lies on side $BC$. Let $O$, $O_1$, and $O_2$ be the circumcenters of triangle $ABC$, $ABD$, and $ACD$, respectively. Prove that circumcircles of triangles $BOO_1$ and $COO_2$ meet on line $BC$.