Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 7 - Section 7.2 - Concurrence of Lines - Exercises - Page 326: 42

Answer

Since all three sides are congruent, $~~\triangle AOF \cong \triangle AOE~~$ by SSS

Work Step by Step

We can show that the three sides of the triangles are congruent. $OF \cong OE$ since both line segments are radii of the circle. $AO \cong AO$ by identity since they are the same line segment. Note that $\angle AFO \cong \angle AEO = 90^{\circ}$, since the line segments $AB$ and $AC$ are tangent to the circle. Then, using the Pythagorean Theorem, we can show that $AF \cong AE$: $\overline{AF} = \sqrt{(AO)^2-(OF)^2} = \sqrt{(AO)^2-(OE)^2} = \overline{AE}$ Since all three sides are congruent, $~~\triangle AOF \cong \triangle AOE~~$ by SSS
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