The Circle

A circle is the set of all points the same distance from a fixed centre — a polygon with infinitely many sides. Learn the radius, diameter, and the circumference formula C = 2πr = πd.

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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.

6 sides 12 sides ∞ (circle)
Theorem Parts of a circle
O r d

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 .

Theorem Circumference

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

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

Example Finding the circumference

From the radius

A circle has radius .
.
⟹ C ≈ 345.6.

From the diameter

A circle has diameter , so .
.
⟹ C ≈ 62.8.
Summary
  1. A circle is the set of all points at a fixed distance r from a centre — a polygon with infinitely many sides.
  2. The radius r reaches from the centre to the circle; the diameter is .
  3. The diameter is the longest chord of the circle.
  4. The circumference is , with .
283. Relations and Functions
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