Answer: 6.9
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Work Shown:
(tangent)^2 = (whole secant)*(external secant)
(TU)^2 = (RT)*(ST)
(TU)^2 = (RS+ST)*(ST)
(TU)^2 = (8+4)*(4)
(TU)^2 = 48
TU = sqrt(48)
TU = 6.928203
TU = 6.9
For more info, you can search out "secant tangent chord", or something similar, and you should get to a page that describes the formula of what's going on here. This should match up fairly similarly to what lesson 3.09 is talking about.