Question 197
Let $\triangle ABC$ be a scalene triangle. Let $h_{a}$ be the locus of points $P$ such that $|PB - PC| = |AB - AC|$. Let $h_{b}$ be the locus of points $P$ such that $|PC - PA| = |BC - BA|$. Let $h_{c}$ be the locus of points $P$ such that $|PA - PB| = |CA - CB|$. In how many points do all of $h_{a}$, $h_{b}$, and $h_{c}$ concur?