Question 102
In an acute $\triangle ABC$ the altitudes $AA_1$ ($A_1 \in BC$) and $BB_1$ ($B_1 \in AC$) are drawn, $I$ is the incenter and the line $CI$ meets $AB$ at $L$. It is known that $I$ lies on the circumcircle of $\triangle A_1B_1C$.
a) Prove that $L$ is the center of excircle of $\triangle A_1B_1C$ tangent to the side $A_1B_1$.
b) If $CI = 2IL$, find $\measuredangle ACB$.
a) Prove that $L$ is the center of excircle of $\triangle A_1B_1C$ tangent to the side $A_1B_1$.
b) If $CI = 2IL$, find $\measuredangle ACB$.