MathNet 2018-part-07 — 177 problems (EN–VI) Question 89

Triangle $\triangle ABC$ has $AB = 21$, $BC = 55$, and $CA = 56$. There are two points $P$ in the plane of $\triangle ABC$ for which $\angle BAP = \angle CAP$ and $\angle BPC = 90^{\circ}$. Find the distance between them.