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 \(100m+n\).
by
Alexander Katz