BdMO National 2012: Junior 9

[Zzzz]

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 $\frac{AS}{SB}=\frac{bc}{2aR}$

[Phlembac Adib Hasan]

($8585^{th}$ post) For a hint :viewtopic.php?f=25&t=1659

[Tahmid Hasan]

Brahmagupta