Two Circles with centers $O_1$ and $O_2$ are tangent exterior at point T. Let points A and B be on the common tangent line through T such that T is between A and B. The tangent lines from A and B to circle $O_1$ meet at point M and the tangent line from A and B to circle $O_2$ meet at point N.
Prove that AM+BN=AN+BM
I know that ATB is the radical axis of the two circles. I am assuming the proof is about power of the point of points M, N, A, and B. Any help would be appreciated!