MathNet 2023-part-07 — 187 problems (EN–VI) Question 151

Let $ABCD$ be a convex trapezoid such that $\angle BAD = \angle ADC = 90^{\circ}$, $AB = 20$, $AD = 21$, and $CD = 28$. Point $P \neq A$ is chosen on segment $AC$ such that $\angle BPD = 90^{\circ}$. Compute $AP$.