Question 24
Let $XY$ be a diameter of a circle $\omega$ of radius 10 cm centered at $O$. Let $A$ and $B$ be the points on $XY$ such that $X,A,O,B,Y$ are in this order and $AO=OB=4$ cm. Suppose that $P$ is a point on $\omega$ such that the lines $PA$ and $PB$ intersect $\omega$ at $C$ and $D$ respectively with $C$ and $D$ distinct from $P$. Given $\dfrac{PB}{BD}=\dfrac{16}{21}$, determine the ratio $\dfrac{PA}{AC}$.