Circle Anatomy and Vocabulary

What is circle anatomy?

You've been handed a paint roller and a job: repaint the centre faceoff circle at the rink. The plans say the circle is 9 m across. Your only tools are a peg, a string, and the roller. How long do you cut the string — 9 metres? Cut it that long and you'll paint a circle eighteen metres wide, halfway into the bleachers. This lesson is about why, and it comes down to three words that sound interchangeable and aren't: radius, diameter, circumference.

Start with the object itself. A circle is a 2-D shape made from all points that are the same distance from one point, the centre.

The size of a circle is determined by its radius.

The radius is a line segment from the centre to the circle. The diameter goes all the way across the circle through the centre, so its length is twice the radius:

The circumference is the perimeter of a circle. It is the distance around the outside edge.

Draw it from the radius

To create a circle with a compass, place the compass point at the centre and open the compass to the radius. When the pencil turns around the centre, every point it draws is the same distance from that centre.

That is why the radius controls the circle. A radius of 3 cm makes a smaller circle than a radius of 6 cm; doubling the radius doubles the diameter too.

Now take the compass yourself. The builder below hands you three build orders, and only one of them states the radius outright — the other two make you convert first. The compass has exactly one setting, and it is always a radius. No target is shown while you work: the order's numbers are all you get. Commit to an opening, draw — and only then does the target appear to judge you.

Where it shows up in real life

A hockey rink has centre faceoff circles. A regulation centre faceoff circle has a diameter of 9 m.

The radius is half the diameter:

So if someone paints the circle from its centre, the painter needs a 4.5 m radius. If someone measures across the whole circle through the centre, they should get a 9 m diameter.

Misconception probe

Worksheet

These are not graded. Use them to check whether each circle word is attached to the right part of the diagram.

Going further

The next circle lesson measures the outside edge. Once the diameter is known, the circumference is not random: every circle has the same circumference-to-diameter relationship. That special relationship is called pi.