Chapter 8.CR, Problem 36CR

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# Given : Concentric circles with radii of lengths R and r, with R > r Prove : A r i n g = π ( B C ) 2

To determine

To prove:

Aring=π(BC)2

Explanation

Calculation:

Consider the diagram as shown below:

Lengths of the radii of the above concentric circles are R and r with R>r.

Join the line segment OCÂ¯, this is the radius of the outer circle.

We call r the radius of the smaller circle. The radius of the larger circle is:

R=BC2+r2R2=BC2+r2

Area of the shaded region is subtracting the area of the small circle from the area of the larger circle.

Thus, the area of the ring is:

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