   Chapter 6.CR, Problem 27CR 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 Review Exercises 27 to 29, give a proof for each statement. G i v e n :                     D C -   i s   t a n g e n t   t o   c i r c l e s   B   a n d   A   a t   p o i n t s   D   a n d   C ,   r e s p e c t i v e l y             P r o v e :                   A C · E D = C E · B D To determine

To Prove: AC·ED=CE·BD, if DC- is tangent to circles B and A at points D and C, respectively. Explanation

Concept:

Theorem 6.2.3: The radius (or any other line through the center of a circle) drawn to a tangent at the point of tangency is perpendicular to the tangent at that point.

Calculation:

Given that DC- is tangent to circles B and A at points D and C, respectively.

By theorem 6.2.3, BDDE and ACCE.

So, BDE=ACE=90°

Because vertically opposite angles are equal, BED=AEC

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