   Chapter 6.CT, Problem 12CT 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, T V ¯ is a tangent and Δ T V W ∼   Δ T X V . Find T V if T X = 3 and X W = 5 . To determine

To find:

TV from, .

Explanation

Given:

TV¯ is a tangent and ΔTVWΔTXV.

TX=3 and XW=5.

Theorem used:

“ 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”.

Calculation:

Consider,

From the 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” we can have,

TV2=TXTW(1).

Here,

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