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.

In an equilateral triangle, the angle bisector and perpendicular bisector are the same line. Since triangle PQR is an equilateral triangle with all sides equal to 9, we can conclude that XY is also equal to 9.