8. In the triangle $A B C$, the bisectors of $\angle A$ and $\angle B$ meet at the incentre $I$, the extension of $A I$ meets the circumcircle of triangle $A B C$ at $D$. Let $P$ be the foot of the perpendicular from $B$ onto $A D$, and $Q$ a point on the extension of $A D$ such that $I D=D Q$. Determine the value of $(B Q \times I B) /(B P \times I D)$.