In the figure, line TU is tangent to the circle at point U. Use the figure to answer both of the questions. Show all of your work.(a) Describe the relationship among the lengths of the segments formed by the secant, RT , and the tangent segment, TU. You may use words and/or an equation to describe. (b) Suppose RT= 9 in. and ST = 4 in. Is it possible to find the length of TU ? If so, show how to find the length. If not, explain why not.

Accepted Solution

a) By the secant rules for circles,
  RT×ST = TU²

b) Using the above relationship, fill in the given values and solve for TU.
  (9 in)×(4 in) = TU²
  TU = √(36 in²) = 6 in