The circle centered at \((2,-1)\) and with radius \(4\) intersects the circle centered at \((2,5)\) and with radius \(\sqrt{10}\) at two points \(A\) and \(B\). Find \((AB)^2.\)
The coordinates of the intsersection are ((24 + sqrt(455))/12, 31/12) and ((24 - sqrt(455))/12, 31/12). Then AB = sqrt(455)/6, so the answer is 455/36.
