MathNet 2015-part-03 — 191 problems (EN–VI) Question 49

$ABCD$ is a trapezium with $AB \parallel CD$, $AB = 42$, $BC = 20$ and $DA = 15$. $P$ is a point on $AB$, and a circle with centre $P$ is tangent to both $BC$ and $AD$. Find $PA \times PB$.