RU-ALLRUSSIAN 2017 Problem 108

In a non-isosceles triangle $ABC$ , $O$ and $I$ are circumcenter and incenter,respectively. $B^\prime$ is reflection of $B$ with respect to $OI$ and lies inside the angle $ABI$ .Prove that the tangents to circumcirle of $\triangle BB^\prime I$ at $B^\prime$ , $I$ intersect on $AC$ . (A. Kuznetsov)