Question 173
Let $ABC$ be a triangle all of whose angles are acute.
The altitudes $[AA_{1}]$, $[BB_{1}]$ and $[CC_{1}]$ meet at point $H$. Let $A_{2}$ be the reflection of $A$ in $[B_{1}C_{1}]$, and let $O$ be the circumcenter of $ABC$.
a) Prove that the points $O, A_{2}, B_{1}, C$ are concyclic.
b) Prove that $O, H, A_{1}, A_{2}$ are concyclic.
The altitudes $[AA_{1}]$, $[BB_{1}]$ and $[CC_{1}]$ meet at point $H$. Let $A_{2}$ be the reflection of $A$ in $[B_{1}C_{1}]$, and let $O$ be the circumcenter of $ABC$.
a) Prove that the points $O, A_{2}, B_{1}, C$ are concyclic.
b) Prove that $O, H, A_{1}, A_{2}$ are concyclic.