TUYMAADA 2008 S3

Point $I_1$ is the reflection of incentre $I$ of triangle $ABC$ across the side $BC$ . The circumcircle of $BCI_1$ intersects the line $II_1$ again at point $P$ . It is known that $P$ lies outside the incircle of the triangle $ABC$ . Two tangents drawn from $P$ to the latter circle touch it at points $X$ and $Y$ . Prove that the line $XY$ contains a medial line of the triangle $ABC$ .

Author: L. Emelyanov