Question 82
Let $A_1$ and $B_1$ be points on the sides $AC$ and $BC$ of $\triangle ABC$ such that $4 AA_1 \cdot BB_1 = AB^2$. If $AC = BC$, prove that the line $AB$ and the bisectors of $\measuredangle AA_1B_1$ and $\measuredangle BB_1A_1$ are concurrent.