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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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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 . _

Chapter 6.CT, Problem 12CT, In the figure, TV is a tangent and TVWTXV. Find TV if TX=3 and XW=5. _

To determine

To find:

TV from,

Elementary Geometry for College Students, Chapter 6.CT, Problem 12CT .

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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