   Chapter 6.3, Problem 24E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In the figure for Exercises 21 to 24, R S ¯ is tangent to the circle at S. See Theorem 6.3.7.Given: R T = 1 2 ⋅ R S     a n d     T V = 9 Find: RT. To determine

To find:

The value of RT

Explanation

Given that, RT=12RSandTV=9

The diagrammatic representation is given below,

Theorem:

If a tangent segment and a secant segment are drawn to a circle from an external point, then the square of the length of the tangent equals the product of the length of the secant with the length of its external segment.

By using the theorem to get the following,

RS2=RVRT

We know that

RV=RT+TVRV=12RS+9

Substitute the values RT=12RSandRV=12RS+9 in the above equation to get the following,

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