   Chapter 6.3, Problem 27E 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 Exercises 27 to 30, provide a paragraph proof.Given: ⊙ O     a n d     ⊙ Q are tangent at point FSecant A C   ¯   t o     ⊙ O Secant A E   ¯   t o     ⊙ Q Common internal tangent A F ¯ Prove: A C ⋅ A B = A E ⋅ A D To determine

To find:

Explanation

Given that, OandQ are tangent at point F, Secant AC¯toO, Secant AE¯toQ.

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 for the circle O to get the following,

AF2=ACAB

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