Critical Radius

An ellipse has the equation

$\dfrac{x^2}{9} + \dfrac{y^2}{4} = 1$

And a family of circles centered at $(5, 6)$ is given by

$(x - 5)^2 + (y - 6)^2 = r^2$

For two critical values of $r$ the circle and the ellipse intersect at a single point. Find the sum of these two values of $r$