SHARYGIN 2020 Problem 13

Let $I$ be the incenter of triangle $ABC$ . The excircle with center $I_A$ touches the side $BC$ at point $A'$ . The line $l$ passing through $I$ and perpendicular to $BI$ meets $I_AA'$ at point $K$ lying on the medial line parallel to $BC$ . Prove that $\angle B \leq 60^\circ$ .