Question 121
An equilateral triangle $ABC$ is inscribed into a circle $\Omega$ and circumscribed about a circle $w$. Points $P$ and $Q$ are chosen on the sides $AC$ and $AB$, respectively, so that the segment $PQ$ is tangent to $w$. A circle $\Omega_b$ centered at $P$ passes through $B$, and a circle $\Omega_c$ centered at $Q$ passes through $C$. Prove that the circles $\Omega$, $\Omega_b$, and $\Omega_c$ have a common point.