Question 67
Let $ABCD$ be a cyclic quadrilateral with an incircle of radius $6$. Let the extensions of sides $AB$ and $DC$ beyond $B$ and $C$, respectively, meet at $P$, and let the extensions of sides $AD$ and $BC$ beyond $D$ and $C$, respectively, meet at $Q$. The inradii of triangle $PBC$ and $QCD$ are $5$ and $3$, respectively. Find $\frac{BC}{CD}$.