Question 54
The acute triangle $ABC$ and the triangle $A_1B_1C_1$, whose vertices $B_1$, $C_1$ and $A_1$ lie on the rays $AC$, $BA$ and $CB$, respectively, are similar. Prove that the orthocenter of the triangle $A_1B_1C_1$ and the circumcenter of the triangle $ABC$ coincide.