RU-SPB 2019 Problem 96

The bisectors $BB_1$ and $CC_1$ of the acute triangle $ABC$ intersect in point $I$ . On the extensions of the segments $BB_1$ and $CC_1$ , the points $B'$ and $C'$ are marked, respectively So, the quadrilateral $AB'IC'$ is a parallelogram. Prove that if $\angle BAC = 60^o$ , then the straight line $B'C'$ passes through the intersection point of the circumscribed circles of the triangles $BC_1B'$ and $CB_1C'$ .