IR-TST 2014 Problem 13

The incircle of a non-isosceles triangle $ABC$ with the center $I$ touches the sides $BC,AC,AB$ at $A_{1},B_{1},C_{1}$ . let $AI,BI,CI$ meets $BC,AC,AB$ at $A_{2},B_{2},C_{2}$ . let $A'$ is a point on $AI$ such that $A_{1}A'\perp B_{2}C_{2}$ . $B',C'$ respectively. prove that two triangle $A'B'C',A_{1}B_{1}C_{1}$ are equal.