MathNet 2017-part-05 — 176 problems (EN–VI) Question 111

Let $O$ and $I$ be respectively the circumcenter and the incenter of a scalene triangle $ABC$. Let $B'$ be the point symmetric to $B$ with respect to the line $OI$; we assume that $B'$ lies inside the angle $ABI$. Prove that the tangents to the circumcircle of the triangle $BIB'$ at points $B'$ and $I$ meet on the line $AC$.
(A. Kuznetsov)