In triangle PQR, let X be the intersection of the angle bisector of angle P with side QR, and let Y be the foot of the perpendicular from X to line PR. If PQ = 9, QR = 9, and PR = 9, then compute the length of XY.
\(\mbox{XY=} \frac{180}{4} \mbox{=} \mbox{45} \)
