A circle is the set of all points that are the same distance from one fixed point. That fixed point is the centre and that fixed distance is the radius. Every single word in this unit is just a name for something that one rule produces.
A compass holds two things a fixed distance apart, pins one down, and drags the other around. That is the definition of a circle acted out with metal. A nail, a string and a pencil do exactly the same job.
The names, and where each one comes from
| Name | What it is |
|---|---|
| Centre | The fixed point everything is measured from. It is not part of the circle itself |
| Radius | A straight line from the centre to the circle. Every radius of one circle is the same length |
| Diameter | A chord that passes through the centre. It is the longest chord, and it is two radii in a straight line |
| Chord | Any straight line joining two points on the circle |
| Arc | A piece of the circle itself, the curved part between two points |
| Sector | The slice of pizza shape: two radii and the arc between them |
| Segment | The piece cut off by a chord. Not a slice from the centre, but a slice off the edge |
| Circumference | The whole way round the outside. It is the circle's perimeter, given a special name |
A sector is cut with two straight lines from the centre, like a slice of pizza. A segment is cut with one straight line that does not go through the centre, like the piece you get when you slice the top off an orange. A sector always has the centre on its edge; a segment never touches the centre.
The number that never changes
Measure the distance round any circular object with a string, then measure straight across it through the middle, and divide the first by the second. You get a number a little over three, every single time, whatever the size. That number is pi, roughly 3.14 or 22 divided by 7.
Every circle in the universe, from a coin to a planet's orbit, has the same ratio between its way round and its way across. That is because all circles are similar, the idea from Unit 3. One number, the radius, describes a circle completely, so any two circles differ only by a scale factor.
Because the way round divided by the way across is always pi, the way round must be pi times the way across:
\[ C = \pi d \qquad \text{and since } d = 2r, \qquad C = 2\pi r \]
These are not two formulas, they are the same formula written twice, because a diameter is two radii. Use whichever one matches the number the question gave you.
Reading a radius as a diameter, or the other way round, and getting an answer exactly twice or exactly half the correct one. Before you touch the formula, write down which one you have been given.
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Find the circumference of a circle of radius 14 cm. Take pi as 22/7.
A bicycle wheel is 70 cm across. How many turns does it make over 1 kilometre?
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A circle is all the points that are the same distance from one fixed point.
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