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:

Answer 1

The length of segment TU is equal to 10 inches

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)`

substitute the given values

`TU^2=(25)(4)`

`TU^2=100\\TU=10\ in`