In triangle $pqr,$ the side lengths are $pq = 9,$ $pr = 10,$ and $qr = 17. $ let $x$ be the intersection of the angle bisector of $\angle p$ with side $\overline{qr}$, and let $y$ be the foot of the perpendicular from $x$ to side $\overline{pr}$. Compute the length of $\overline{xy}$.

Alex is the head photographer for the yearbook and the newspaper. she has a large staff of assistant photographers because they need to take pictures at all of the school events. she knows that some of her photographers have better cameras and can take action shots at sporting events, and that some of them are good at taking candid pictures in the hallways. she sets firm deadlines so she has enough time to look through all of the shots and choose the best ones. she gives her photographers constructive feedback to them improve their pictures. respectful enforcer warlord doormat peacemaker