Circles and the compass

Builders need bricks and cement; in this chapter your materials are a ruler and a compass. First, mark a point P in your notebook. Then mark as many points as you can, in different directions, that are all 4 cm away from P. Now imagine marking ALL the points that are exactly 4 cm from P. What shape would they make?

They make a circle! Every point on the circle is the same distance, 4 cm, from P.

• The point P is called the centre of the circle.
• The distance from the centre to any point on the circle is called the radius. Here the radius is 4 cm.

A point inside the circle is less than 4 cm from P; a point outside is more than 4 cm from P.

A compass draws such a circle for you.

• First set the compass: open it against a ruler so that the distance between the metal point and the pencil tip is 4 cm.
• Then put the metal point on P and keep it fixed; move only the pencil, turning it all the way round.

Because the opening does not change, every point the pencil draws is 4 cm from P.

The compass can also draw just part of a circle, called an arc: stop turning before you get all the way round. A compass can also copy a length: open it to the length once, and you can mark that same length anywhere. You will use arcs a lot in this chapter.