Question 96
Let $ABC$ be a scalene acute triangle. Let $B_{1}$ be the point on ray $[AC$ such that $|AB_{1}| = |BB_{1}|$. Let $C_{1}$ be the point on ray $[AB$ such that $|AC_{1}| = |CC_{1}|$. Let $B_{2}$ and $C_{2}$ be the points on line $BC$ such that $|AB_{2}| = |CB_{2}|$ and $|BC_{2}| = |AC_{2}|$. Prove that $B_{1}, C_{1}, B_{2}, C_{2}$ are concyclic.