RU-SPB 2017 Problem 92

Given a triangle $ABC$ , there's a point $X$ on the side $AB$ such that $2BX = BA + BC$ . Let $Y$ be the point symmetric to the incenter $I$ of triangle $ABC$ , with respect to point $X$ . Prove that $YI_B\perp AB$ where $I_B$ is the $B$ -excenter of triangle $ABC$ .