circle

Technical terms used in the geometry of the circle; the area of a circle can be seen to equal πr² by dividing the circle into segments that form a rectangle.

Perfectly round shape, the path of a point that moves so as to keep a constant distance from a fixed point (the centre). A circle has a radius (the distance from any point on the circle to the centre), a circumference (the boundary of the circle, part of which is called an arc), diameters (straight lines crossing the circle through the centre), chords (lines joining two points on the circumference), tangents (lines that touch the circumference at one point only), sectors (regions inside the circle between two radii), and segments (regions between a chord and the circumference).

The ratio of the distance all around the circle (the circumference) to the diameter is an irrational number called π (pi), roughly equal to 3.1416.

A circle of radius r and diameter d has a circumference C = πd, or C = 2πr, and an area A = πr². The area of a circle can be shown by dividing it into very thin sectors and reassembling them to make an approximate rectangle. The proof of A = πr² can be done only by using integral calculus.

Angles within a circle can be calculated using the circle theorems.

Calculating the circumference and area of a circle In the following example, the calculations for the area of a simple dart-board, and the amount of wire needed (comprising an inner and outer circle, and 6 straight pieces) are shown. The radius of the inner circle is 14 cm and the radius of the outer circle is 28 cm:

To find the length of wire:

diameter of outer circle = 2 × radius = 2 × 28 = 56 cm length of 6 straight pieces = 6 × 56 = 336 cm circumference of outer circle = πd = π × 56 = 176 cm circumference of inner circle = πd = π × 28 = 88 cm

Total length of wire = 336 + 176 + 88 = 600 cm or 6 m.

To find the area of board:

area = πr2

Area of board = π × 282 = 2,463 cm2 = 0.2463 m2.