Two ways round
Arcs: major and minor
A circular track
Imagine walking round a circular track from A to B. You can set off one way, or the other way.
Two points A and B are on a circle. How many different ways are there to go from A to B along the circle?
What this lesson covers
The idea
An arc is a connected portion of a circle with two end points; two points on a circle give two arcs, the bigger called the major arc and the smaller the minor arc.
A circular track
Imagine walking round a circular track from A to B. You can set off one way, or the other way.
Two points A and B are on a circle. How many different ways are there to go from A to B along the circle?
- Two
- Just one
- As many as you like
Which way is longer?
Drag A and B round the circle. The arc going anticlockwise from A to B passes the mark X. The other arc passes the mark Y.
Major and minor
An arc is a connected portion of a circle, with two end points. Two points on a circle give two arcs: the bigger is the major arc, the smaller is the minor arc.
Going from A to B via X is one arc, and going via Y is the other. The longer way round is the major arc. The shorter way is the minor arc.
Notes
Two points on a circle give two arcs: the bigger is the major arc and the smaller is the minor arc.
Check yourself
Two points on a circle split it into two arcs, one longer than the other. What is the longer arc called?
A circle has circumference 30 cm. The minor arc AB is 8 cm long. How long is the major arc AB, in cm?
Answer: 22 cm
The minor arc and the major arc together make the whole circle: 30 − 8 = 22 cm.
Which of these is a connected portion of a circle, with two end points?
A and B are points on a circle. The arc from A to B via X is 5 cm long, and the arc via Y is 9 cm long. Which is the major arc?
- The major arc — correct. Yes. The bigger of the two arcs is the major arc.
- The minor arc. The minor arc is the smaller one.
- The chord. A chord is a straight line segment joining two points of the circle. It is not part of the circle.
- A chord. A chord is a straight line segment between two points of the circle. It is not a piece of the circle.
- An arc — correct. Yes. An arc is a connected piece of the circle itself.
- A radius. A radius is a line segment from the centre to the circle. It is not a piece of the circle.
- The arc via Y — correct. Yes. It is the longer of the two arcs.
- The arc via X. The arc via X is the shorter one, so it is the minor arc.
- Neither: they are the same. They are 5 cm and 9 cm, so one is longer than the other.