   Chapter 7.2, Problem 46E 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

For exercises 44 to 46, O is the inscribed circle for ∆ A B C . In exercises 45 and 46, use the result from 44.Where s = 1 2 a + b + c , Show that A F = s - a To determine

To show:

That the incenter triangle AF=s-a

Explanation

Formula used:

Perimeter of incircle:

perimeterofincircle (s)=12(a+b+c)

Given:

Where s=12a+b+c, Show that AF=s-a

Calculation:

Let us consider the incircle triangle,

Let BF=x as shown in the figure.

BF=BD=x Tangents drawn from the same point B to the incircle.

Similarly, CE=CD=z and AE=AF=y

Given that s=12(a+b+c)

s=12((x+z)+(y+z)+(x+y))s=12(2x+2y+2z)s=122(x+y+z)s=x+y+zInterc

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