Point $P$ is taken inside the square $ABCD$ such that $BP + DP=25$, $CP - AP = 15$ and $\angle$ABP = $\angle$ADP. What is the radius of the circumcircle of $ABCD$?
Source: BdMO 2020 Final Primary Category Problem 6
Tags: analytic geometry, geometry
Point $P$ is taken inside the square $ABCD$ such that $BP + DP=25$, $CP - AP = 15$ and $\angle$ABP = $\angle$ADP. What is the radius of the circumcircle of $ABCD$?