INMO 2014 Problem 5

In an acute-angled triangle $A B C$, a point $D$ lies on the segment $B C$. Let $O_{1}, O_{2}$ denote the circumcentres of triangles $A B D$ and $A C D$, respectively. Prove that the line joining the circumcentre of triangle $A B C$ and the orthocentre of triangle $\mathrm{O}_{1} \mathrm{O}_{2} \mathrm{D}$ is parallel to $B C$.