Question 2
Let $ABC$ be a triangle, $I$ its incenter, and $\omega$ a circle of center $I$. Points $A'$, $B'$, $C'$ are on $\omega$ such that rays $IA'$, $IB'$, $IC'$ starting from $I$ intersect perpendicularly sides $BC$, $CA$, $AB$, respectively. Prove that lines $AA'$, $BB'$, $CC'$ are concurrent.