The Circle | Moosa Academy

A circle is the set of all points that lie the same distance from a fixed centre. One neat way to picture it is as a regular polygon with infinitely many sides.

Theorem A circle is a polygon with infinite sides

The more sides a regular polygon has, the closer it looks to a circle. As the number of sides grows without limit, the polygon becomes a circle.

Theorem Parts of a circle

Centre O — the point that is the same distance from every point on the circle.

Radius r — the distance from the centre to any point on the circle.

Diameter d — a chord through the centre, and $d = 2r$ .

Theorem Circumference

The distance around a circle is its circumference, found from the radius or the diameter.

C = 2\pi r = \pi d

Here $\pi$ (pi) is the constant ratio of any circle's circumference to its diameter, about $3.14159$ .

Example Finding the circumference

From the radius

A circle has radius

r = 55

C = 2\pi r = 2\pi(55) = 110\pi \approx 345.6

⟹ C ≈ 345.6.

From the diameter

A circle has diameter

d = 20

, so

r = 10

C = \pi d = 20\pi \approx 62.8

⟹ C ≈ 62.8.

Summary

A circle is the set of all points at a fixed distance r from a centre — a polygon with infinitely many sides.
The radius r reaches from the centre to the circle; the diameter is $d = 2r$ .
The diameter is the longest chord of the circle.
The circumference is $C = 2\pi r = \pi d$ , with $\pi \approx 3.14159$ .