Question 118
Let $P$ be a point outside a circle, and let the two tangent lines through $P$ touch the circle at $A$ and $B$. Let $C$ be a point on the minor arc $A B$, and let $\overrightarrow{P C}$ intersect the circle again at another point $D$. Let $L$ be the line that passes through $B$ and is parallel to $\overline{P A}$, and let $L$ intersect $\overrightarrow{A C}$ and $\overrightarrow{A D}$ at points $E$ and $F$, respectively. Prove that $B$ is the midpoint of $\overline{E F}$.