Let $\Omega$ be the circumcircle of triangle $ABC$ such that the tangents to $\Omega$ in points $B$ and $C$ intersect in $P$. The squares $ABB_1B_2$ and $ACC_1C_2$ are constructed on the sides $AB$ and $AC$ in the exterior of triangle $ABC$, such that the lines $B_1B_2$ and $C_1C_2$ intersect in point $Q$. Prove that $P$, $A$, and $Q$ are collinear.