Question 107
The altitudes $AA_1, BB_1, CC_1$ of the acute triangle $ABC$ intersect at $H$. Let $A_2$ be the reflection of point $A$ in the line $B_1C_1$ and let $O$ be the circumcenter of triangle $ABC$.
a) Prove that the points $O, A_2, B_1, C$ are cocyclic.
b) Prove that the points $O, H, A_1, A_2$ are cocyclic.
a) Prove that the points $O, A_2, B_1, C$ are cocyclic.
b) Prove that the points $O, H, A_1, A_2$ are cocyclic.