In $\bigtriangleup$$ABC$ $BL$ is bisector. Arbitrary point $M$ on segment $CL$ is chosen. Tangent to $\odot$$(ABC)$ at $B$ intersects $CA$ at $P$. Tangents to $\odot$$BLM$ at $B$ and $M$ intersect at point $Q$. Prove that $PQ$$\parallel$$BL$.
Source: 2016 Russian Regional Olympiad
Tags: geometry
In $\bigtriangleup$$ABC$ $BL$ is bisector. Arbitrary point $M$ on segment $CL$ is chosen. Tangent to $\odot$$(ABC)$ at $B$ intersects $CA$ at $P$. Tangents to $\odot$$BLM$ at $B$ and $M$ intersect at point $Q$. Prove that $PQ$$\parallel$$BL$.