Question 166
The circles $O_1$ and $O_2$ meet at points $A$ and $B$. The line $DC$ passes through $O_1$, intersects the circle $O_1$ at $D$ and is a tangent to the circle $O_2$ at $C$. Also, $CA$ is a tangent to the circle $O_1$ at $A$. The secant $AE$ of the circle $O_1$ is perpendicular to $DC$. $AF$ is perpendicular to $DE$ and meets $DE$ at $F$.
Prove that $BD$ bisects the line segment $AF$. (posed by Bian Hongping)
Prove that $BD$ bisects the line segment $AF$. (posed by Bian Hongping)