Question 93
A semicircle $\Gamma$ has diameter $AB = 25$. Point $P$ lies on $AB$ with $AP = 16$ and $C$ is on the semicircle such that $PC \perp AB$. A circle $\omega$ is drawn so that it is tangent to segment $PC$, segment $PB$, and $\Gamma$. What is the radius of $\omega$?