Question

In the figure, TU is tangent to the circle at point U. Use the figure to answer the questions.

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. (2 points)
Suppose RT=25 in. and ST=4 in. Is it possible to find the length of ? If so, show how to find the length. If not, explain why not. (3 points)

Answer 1

1. Power of point : TU^2 - ST^2 = RS*ST

2. 10

Explanation:

1. By power of point,

RT * ST = TU^2

( RS + ST ) * ST = TU^2

RS*ST + ST^2 = TU^2

TU^2 - ST^2 = RS*ST

2. TU^2 = 25*4 = 100

So, TU = 10