Parts of a circle
- The radius goes from the centre to the edge. The diameter goes right across through the centre and is twice the radius. The circumference is the distance around the circle.
- A chord joins two points on the circle. A tangent touches the circle at one point. An arc is part of the circumference.
- A sector is a 'slice' between two radii. A segment is the region between a chord and an arc.
Circumference and area
- Circumference = πd = 2πr. Area = πr².
- A circle with radius 5 cm has a circumference of 10π = 31.4 cm and an area of 25π = 78.5 cm² (1 d.p.).
- 'Give your answer in terms of π' means leave π in the answer, such as 25π cm².
Arcs and sectors
- A sector with angle θ is θ/360 of the whole circle.
- Arc length = θ/360 × 2πr. Sector area = θ/360 × πr².
- A 90° sector of radius 6 cm has an area of ¼ × 36π = 9π = 28.3 cm² and an arc length of ¼ × 12π = 3π = 9.42 cm.
Semicircles and perimeters
- The perimeter of a semicircle is half the circumference plus the diameter. With radius 4 cm: 4π + 8 = 20.6 cm.
- The perimeter of a sector is the arc length plus two radii.
Key terms
- Radius
- The distance from the centre of a circle to its edge.
- Diameter
- The distance across a circle through its centre; twice the radius.
- Circumference
- The distance around a circle.
- Chord
- A straight line joining two points on a circle.
- Arc
- Part of the circumference of a circle.
- Sector
- The region between two radii and an arc, like a slice of pizza.
- Segment
- The region between a chord and an arc.
- π (pi)
- The circumference of any circle divided by its diameter, about 3.14159.