Question 93
The incircle of $\triangle ABC$ has center $I$ and touches the sides $BC$, $AC$ and $AB$ at points $A_1$, $B_1$ and $C_1$, respectively. An arbitrary line $\ell$ through $I$ is given and the points $A'$, $B'$ and $C'$ are symmetric to $A_1$, $B_1$ and $C_1$, respectively, with respect to $\ell$. Prove that the lines $AA'$, $BB'$ and $CC'$ are concurrent.