Fundamentals of Math

Fundamentals of Mathematics

5.6 Properties of Circles

A circle is a figure which has no straight edges or vertices. More formally defined as a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center). This fixed distance is the radius (the distance from the center of the circle to its outer rim), and the fixed point is the circle's center — their center point names the circle. Any line segment whose endpoints are on the circumference of a circle is considered a chord (a chord does not have to go directly through the center of the circle). However, the chord that passes through the center of the circle is the diameter . The diameter is the largest chord a circle has. Diameters are also made up of two radii.

Circumference of a Circle Similar to polygons, we may be interested to know the length of the edge of the circle. The perimeter of a circle is known as the circumference ; it is a definite length equal to twice the radius (or the diameter) multiplied by pi ( ≈ 3.14159 … is a constant) – = = .

Example 5.6.1

To find the circumference of the circle multiply the radius times 2 .

= 2 = 2 (12) = 24

12

Note because is irrational we cannot calculate the exact circumference unless we substitute in an approximation of . If the question doesn’t state what they are seeking leave your answer in terms of like you see here (the exact answer is 24 ). If you are asked to find an approximation then it is okay to substitute in 3.14 for , so 24 → 24(3.14) ≈ 75.36 .

Area of a Circle Likewise, we can also find the area of a circle using the formula pi times the radius squared ( = 2 )

Example 5.6.2

To find the area of the circle square the radius and multiply it times .

2 = (12) 2 = 144

=

12

Like we noted above. If the question doesn’t specify then leave your answer as an exact answer in terms of (144 ). Only substitute in 3.14 for if explicitly told to do so - 144 → 144(3.14) ≈ 452.16 .

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