Question 16
Let $\omega$ be a circle with center $O$ and diameter $AB$. A circle with center $B$ intersects $\omega$ at $C$ and $AB$ at $D$. The line $CD$ intersects $\omega$ at the point $E$ ($E \neq C$). The intersection of lines $OE$ and $BC$ is $F$.
a. Prove that the triangle $OBF$ is isosceles.
b. Find the ratio $\frac{FB}{BD}$, given that $D$ is the midpoint of $OB$.
a. Prove that the triangle $OBF$ is isosceles.
b. Find the ratio $\frac{FB}{BD}$, given that $D$ is the midpoint of $OB$.