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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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BuyFindarrow_forward

Elementary Geometry For College St...

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

In Exercises 46 to 49, prove the stated theorem.

If two secant segments are drawn to a circle from an external point, then the products of the length of each secant with the length of its external segment are equal. See Figure 6.51 on page 303.

To determine

To find:

To prove the following stated theorem,

“If two secant segments share the same endpoint outside a circle, then the product of the length of one secant segment and the length of its external segment equals the product of the length of the other secant segment and the length of its external segment.”

Explanation

Given that tangent EB¯andED¯ are secant segemnts.

To prove EAEB=ECED(PS)2=PRPQ

The diagrammatic representation is given below,

First, draw AD¯andBC¯.

Here BandD intersect the same arc, so BD

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