Question 3
Let $A_1,B_1$ be two points on the base $AB$ of an isosceles triangle $ABC$, with $\angle C\gt 60^\circ$, such that $\angle A_1CB_1=\angle ABC$. A circle externally tangent to the circumcircle of $\triangle A_1B_1C$ is tangent to the rays $CA$ and $CB$ at points $A_2$ and $B_2$, respectively. Prove that $A_2B_2=2AB$.