Question 51
Given a point $p$ and a line segment $l$, let $d(p, l)$ be the distance between them. Let $A$, $B$, and $C$ be points in the plane such that $AB = 6$, $BC = 8$, $AC = 10$. What is the area of the region in the $(x, y)$-plane formed by the ordered pairs $(x, y)$ such that there exists a point $P$ inside triangle $ABC$ with $d(P, AB) + x = d(P, BC) + y = d(P, AC)$?
