Question 8
Triangle $ABC$ has $AB=1$, $BC=\sqrt{7}$, and $CA=\sqrt{3}$. Let $\ell_1$ be the line through $A$ perpendicular to $AB$, $\ell_2$ the line through $B$ perpendicular to $AC$, and $P$ the point of intersection of $\ell_1$ and $\ell_2$. Find $PC$.