Geometry · Quick Reference

Circles Cheat Sheet

Geometry · Lesson 7/16

In one line: a circle is the set of all points the same distance from a fixed center point — one of the most elegant and useful shapes in all of geometry.

Key Ideas

1Radius. The distance from the center of a circle to any point on the circle.

2Diameter. The distance across the circle through its center; the diameter is always twice the radius.

3Circumference. The distance around the outside of a circle, calculated as 2*pi*r or pi*d.

4Area of a Circle. The space enclosed by a circle, calculated as pi*r^2.

5Chord, Arc, and Sector. A chord connects any two points on the circle. An arc is a portion of the circle's edge. A sector is a 'pie slice' region bounded by two radii and an arc.

Worked Examples

Find the circumference of a circle with radius 7 (use pi ~ 3.14).

Approximately 43.96 units

Find the area of a circle with radius 5 (use pi ~ 3.14).

78.5 square units

A circle has diameter 20. Find its radius and circumference (use pi ~ 3.14).

Radius = 10, Circumference = 62.8 units

Formulas

Circumference = 2*pi*r = pi*d

Area = pi*r^2

Practice Yourself

Find the circumference of a circle with radius 10 (pi~3.14).

62.8

Find the area of a circle with radius 4 (pi~3.14).

50.24

A circle has diameter 14. Find its radius.