Proof related to circle

Question

How can I prove that if two circles, one entirely inside the other, intersect at a point, then that point of intersection must be collinear with the centers of the two circles?

Answer 1

By symmetry: mirror the two circles around the line that joins the centers. This leaves the circles unchanged, and so must remain the intersection, so it is on the axis.

Answer 2

Let the radii be AB and and PB. So AB can be written as AP+PB= which proves the collinearity othese 3 points thus both the radii lie on the same line and and the point too. Theres no rigorous proof for this Sorry.