Question

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

Describe the relationship among the lengths of the segments formed by the secant RT, and the tangent Suppose RT=16 in. and ST=4 in. Find the length of . Show your work.

Answer 1

The length of TU is
`8\ in`

Explanation:

we know that

The Intersecting Secant-Tangent Theorem states that, if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment

so

in this problem

`TU^(2)=RT*ST`

we have

`RT=16\ in`

`ST=4\ in`

`TU^(2)=(16)(4)`

`TU^(2)=64`

`TU=8\ in`