Question 145
Let $AB$ be the diameter of a semicircle $\Gamma$. Two circles, $\omega_1$ and $\omega_2$, externally tangent to each other and internally tangent to $\Gamma$, are tangent to the line $AB$ at $P$ and $Q$, respectively, and to semicircular arc $AB$ at $C$ and $D$, respectively, with $AP \lt AQ$. Suppose $F$ lies on $\Gamma$ such that $\angle FQB = \angle CQA$ and that $\angle ABF = 80^\circ$. Find $\angle PDQ$ in degrees.