Question 23
In a triangle $ABC$, we suppose that points $D$ and $E$ lie on the segments $AB$ and $AC$, respectively. Let $D$, $B$, $C$, $E$ lie on the same circumference and let point $P$ lie inside quadrilateral $DBCE$ with $\angle BDP = \angle BPC = \angle PEC$. Calculate $\frac{BP}{CP}$, given that $AB = 9$, $AC = 11$, $DP = 1$ and $EP = 3$.