Circles are everywhere you look — a bike wheel, a clock face, a pizza, the round dish of a satellite antenna. Whenever engineers and designers work with something round, they describe it with a shared set of names, and this page teaches you that vocabulary.

Before you can pull off a single one of the famous circle theorems — those almost-magical shortcuts for finding angles and lengths inside a circle — you need the vocabulary. A circle looks like the simplest shape on Earth: one smooth curve, no corners. But it is secretly packed with named parts — radius, diameter, chord, arc, sector, segment, tangent, circumference — and every rule you will ever meet is written in those words.

Think of it like learning the pieces on a chessboard. Once you know a bishop from a knight, the rules make sense. Muddle the pieces up and nothing works. So let's learn the alphabet of the circle first. Get these eight words straight and the rest of circle geometry unlocks.

From the centre out

A circle is the set of all points the same distance from one fixed point. That fixed point is the centre, usually labelled O. Everything else is measured from there.

• a radius is a straight line from the centre out to the edge — its length is that fixed distance (plural: radii);
• a diameter is a straight line right across the circle through the centre. It is made of two radii end to end, so it is twice the radius: d = 2r;
• a chord is any straight line joining two points on the edge (a diameter is just the longest chord — the one that happens to pass through the centre);
• the circumference is the distance all the way around the edge — the circle's perimeter.

Pieces of the circle

Once we can name the edge and the centre, we can name the pieces we cut out too:

• an arc is part of the edge — a curved piece of the circumference. The shorter one is the minor arc, the longer one the major arc;
• a sector is the "pizza slice" between two radii (the region enclosed by two radii and the arc between them);
• a segment is the region cut off by a chord — the flatter piece between a chord and the arc (like the crust-less bit above a straight cut);
• a tangent is a straight line that just touches the circle at exactly one point, without crossing it.

See them on one circle

Step through the figure to add one part at a time — the centre, a radius, the diameter, a chord, a sector and finally a tangent. Watch how each one sits.

Worked examples

Let's use the words on real figures. The trick is always to ask two questions: does this line pass through the centre? and what is it bounded by?

Example 1 — label the parts. A pizza is cut so that one straight slice runs right through the middle, and a second, shorter straight cut joins two points on the crust without touching the middle. Name each cut.

• The long cut passes through the centre → it is a diameter.
• The short cut joins two edge points but misses the centre → it is a chord.
• The curved crust between the ends of the short cut → an arc.

Example 2 — sector or segment? You cut a single triangular slice with the point at the very middle. What shape is the slice, and what is the leftover cap next to the crust?

• The slice is bounded by two radii and an arc → it is a sector.
• If instead you had sliced straight across with one chord, the flatter piece left above the cut would be a segment.

Example 3 — diameter and radius by number. A bicycle wheel has a radius of r = 34\text{ cm}. How wide is the wheel across the middle?

And going the other way: a clock face is d = 30\text{ cm} across, so its radius is r = d \div 2 = 15\text{ cm}. Diameter and radius are just a doubling and a halving apart.