Geometry question

By power of a point, TU = 6*sqrt(3).

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.

First  case:  both radii are identical:  r = 7.5

                                                         TU = 12 

Second  case:  radii  are different:    r₁ = 5     r₂ =  13.094

The result is the same:                      TU = 12       

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.

https://latex.artofproblemsolving.com/c/5/0/c50a548001dc09c6eb63031398f6a77787276a50.png

answer see: https://web2.0calc.com/questions/welp-number-3