Circular locus

Level 2

The sides of triangle $ABC$ are $5,6,$ and $7$. $P$ is a point in the plane of the triangle such that $PA^2 + PB^2 + PC^2 = 70$. The locus of $P$ is a circle of radius $r$, where $r$ can be expressed in the form $\frac{m}{n}$ for some relatively prime positive integers $m$ and $n$. Find $100m+n$.

×