   Chapter 6.CR, Problem 34CR ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
4 views

# G i v e n :                   ⊙ O   i s   i n s c r i b e d   i n   ∆ A B C                                                             A B = 9 ,   B C = 13 ,   A C = 10       F i n d :                           A D ,   B E ,   F C To determine

To Find: AD, BE, FC if O is inscribed in ABC and AB=9, BC=13, AC=10. Explanation

Concept:

Theorem 6.3.4:

The tangent segments to a circle from an external point are congruent.

Calculation:

Given that O is inscribed in ABC and AB=9, BC=13, AC=10.

Let A,B, and C be vertices of the triangle.

AB,BC, and CA are the sides of the triangle.

Also, AB,BC,  and CA are the tangents of the circle at D, E and F respectively.

By Theorem 6.3.4:

The tangent segments to a circle from an external point are congruent.

Because AB=9, BC=13, AC=10

y+z=9

x+z=13

x+y=10

ABC is right triangle,

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