## Circles

A circle is a shape formed by a curve such that all points on the curve are the same distance from a fixed point, called the centre.

### Definitions

 The circumference is the distance around a circle. A radius is the distance from the centre to any point on the circumference. A diameter is a chord that passes through the centre.The length of the diameter is twice the length of the radius. An arc is a part of the circumference. A chord is a straight line joining two points on the circumference. A segment is an area of a circle bounded by a chord and the circumference. A sector is an area of a circle bounded by two radii and the circumference. A tangent is a line that touches the circumference of a circle at only one point.

### π (Pi) π is a fixed number (called a constant). It is the ratio of the length of the circumference to the length of the diameter. This ratio is the same for ALL circles.

π is an irrational number and cannot be calculated exactly but is equal to 3.141592 (to 7 significant figures)

A good fractional approximation to π is 227.

### Circumference The perimeter of a circle is called the circumference C = 2π r = π d

### Area

 Area of Circle A = π r2

### Examples of Circle Calculations

 Example 1 Circumference Area Find the circumference and area of a circle of radius 6 cm. Use π = 3.1 C = 2π r C = 2 × 3.1 × 6 C = 37.2 cm A = π r2 A = 3.1 × 6 × 6 A = 111.6 cm2 Example 2 Find the area of the sector shown below if the radius of the circle is 8 cm. Use π = 3.1 Angle of sector = 90° Fraction of circle = 90⁄360 = 1⁄4 Area of sector = 0.25 × Area of circle = 0.25 × πr2 = 0.25 × 3.1 × 82 = 49.6 cm2 Example 3 Find the radius of a circle that has a circumference of 55.8 cm. (Use π = 3.1) C = 2πr 55.8 = 2 × 3.1 × r 6.2r = 55.8 r = 55.8⁄6.2 r = 9 cm