Question

Quick math question! Please help!?

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

http://prntscr.com/ixb298

(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 R T = 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.

Answer 1

see explanation.

Explanation:

(a):
According to tangent-secant theorem:
"When a tangent and a secant are drawn from one single external point to a circle, square of the length of tangent segment must be equal to the product of lengths of whole secant segment and the exterior portion of secant segment."
`=> TU^2=TRxxTS`

(b)
given `RT=9` in and `ST=4` in,
`=> TU^2=RTxxST`,
`=> TU^2=9xx4=36 " in"^2`
`=> TU=+-sqrt36= +-6` in
As `TU` can not be negative,
`=> TU=6` in.

P.S. : Proof of tangent-secant theorem is available in the link below:
https://socratic.org/questions/let-m-be-a-point-and-c-a-circle-m-doesn-t-belong-to-the-c-let-a-and-b-be-points-#471096