Two circles intersect at A and B. A common external tangent is tangent to the circles at T and U, as shown. Let M be the intersection of line AB and TU. If AB = 9 and BM = 3, find TU.
Looking at only the left circle: MB · MA = MT · MT
---> 3 · 12 = MT2
36 = MT2
Therefore, MT = 6
Similarly, for the right triangle: MU = 6
Finally: TU = 12