Question 55
The incircle of the right triangle $ABC$ is tangent to the hypotenuse $AB$ at point $P$ and is tangent to the legs $AC$ and $BC$ at points $Q$ and $R$ respectively. Points $C_1$ and $C_2$ are symmetric to $C$ with respect to the lines $PQ$ and $PR$.
Find the angle $C_1IC_2$ where $I$ is the incenter of the triangle $ABC$. (Mikhail Karpuk)
Find the angle $C_1IC_2$ where $I$ is the incenter of the triangle $ABC$. (Mikhail Karpuk)