MathNet 2023-part-02 — 191 problems (EN–VI) Question 150

$ABCD$ is a trapezium with $AD \parallel BC$, $AD \gt BC$ and $AB = CD$. $P$ is a point in the plane whose distances from $A$, $B$, $C$, $D$ are $1$, $2$, $3$, $4$ respectively. Find $AD : BC$.