Prove that the lengths of the two tangent segments to a circle from a point outside are equal. Use part (a) to prove the following: The two tangonto

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter6: Circles
Section6.3: Line And Segment Relationships In The Circle
Problem 5E: Sketch two circles that have: a No common tangents b Exactly two common tangents c Exactly three...
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1. Prove that the lengths of the two tangent segments to a circle from a point outside are equal.
2. Use part (a) to prove the following: The two tangents from an outside point B touch the circle at F and
G. Another tangent at E on the circle intersects the two tangent segments at C and D. Prove that the
perimeter ofABCD is twice the length of a tangent segment from B. That is,
|BC| + |CD| + |DB| = 2|BF|
Transcribed Image Text:1. Prove that the lengths of the two tangent segments to a circle from a point outside are equal. 2. Use part (a) to prove the following: The two tangents from an outside point B touch the circle at F and G. Another tangent at E on the circle intersects the two tangent segments at C and D. Prove that the perimeter ofABCD is twice the length of a tangent segment from B. That is, |BC| + |CD| + |DB| = 2|BF|
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