Form 2 · Chapter 5

Properties of Circles

Learn the parts of a circle — centre, radius, diameter, chord, arc, sector — and how they relate.

Parts of a circle

A circle is the set of all points that are the same distance from a fixed point called the centre. That fixed distance is the radius (r). A straight line through the centre joining two points on the circle is the diameter (d), and it is always twice the radius.

Key idea / Key idea

Diameter = 2 × radius, so d = 2r and r = d ÷ 2. The diameter is the longest chord in a circle.

Chords, arcs and sectors

A chord is a straight line joining any two points on the circle. An arc is part of the circle's edge (circumference). A sector is the region enclosed by two radii and an arc — like a slice of pizza. A segment is the region between a chord and an arc.

PartDescription
RadiusCentre to the circle
DiameterAcross, through the centre
ChordJoins two points on the circle
ArcPart of the circumference
SectorTwo radii + an arc

Using the relationships

Worked example / Worked example

A circle has a diameter of 18 cm. Find its radius.

r = d ÷ 2 = 18 ÷ 2 = 9 cm.

If instead the radius were 7 cm, the diameter would be d = 2 × 7 = 14 cm.

Remember / Remember

  • All radii of one circle are equal.
  • Diameter = 2 × radius; it is the longest chord.
  • A sector needs two radii and an arc.
  • The circumference is the full distance around the circle.

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