**Problem 9:**

Given triangle $ABC$, the square $PQRS$ is drawn such that $P,\ Q$ are on $BC,\ R$ is on $CA$ and $S$ is on $AB$. Radius of the triangle that passes through $A,\ B,\ C$ is $R$. If $AB = c,\ BC = a,\ CA = b,$ Show that $\frac{AS}{SB}=\frac{bc}{2aR}$