MathNet 2021 — Part 07 Question 29

Let $P$ be a point inside isosceles triangle $ABC$ with $AB = AC$, and let $D, E, F$ be the feet of the perpendicular from $P$ to $BC, CA, AB$, respectively. If $BD = 9$, $CD = 5$, $PE = 2$, $PF = 5$, find $AB$.