Question 76
Let $P$ and $Q$ be points on line $l$ with $PQ = 12$. Two circles, $\omega$ and $\Omega$, are both tangent to $l$ at $P$ and are externally tangent to each other. A line through $Q$ intersects $\omega$ at $A$ and $B$, with $A$ closer to $Q$ than $B$, such that $AB = 10$. Similarly, another line through $Q$ intersects $\Omega$ at $C$ and $D$, with $C$ closer to $Q$ than $D$, such that $CD = 7$. Find the ratio $AD / BC$.