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Circles

INTRODUCTION

Here are a few quick facts that are useful to know about a circle that has radius r:

 diagram of the radius of a circle     

Diameter = 2r
Circumference = 2π r
Area = πr2




Example:
If a circle has an area of 16π, what is its radius?

Solution: 

A = π rbut we have A = 16π 

so  π r2 = 16π

          r2 = 16

            r = 4

THE EQUATION OF A CIRCLE

A circle with radius r centred at the origin has the equation:

x2 + y= r2

A circle whose centre is at the point (a,b) has the equation:

(x - a)+ (y - b)= r2

Example: Consider the circle given by the equation (x - 3)+ (y + 2)= 49

What is the position of it's centre? What is the radius?

Solution:

The centre is at (3, -2).

The radius is 7.

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