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Parts of the Circle

FoundationAQAEdexcelOCR

This free Foundation GCSE Maths worksheet on parts of the circle helps you revise naming the parts of a circle. Questions build from straightforward to exam standard, with full worked answers in the mark scheme — ideal for revision or homework. Suitable for AQA, Edexcel and OCR. Know the radius, diameter, chord, tangent, arc, sector and segment.

Free downloads

These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Topic overview

The parts of a circle each have a specific name, and questions often depend on knowing which is which.

The radius runs from the centre to the edge, and the diameter runs right across through the centre, making it twice the radius. The circumference is the distance all the way around.

Other parts describe regions and lines. A chord joins two points on the edge without passing through the centre; a tangent touches the circle at exactly one point; a sector is a slice between two radii; and a segment is the region cut off by a chord.

Revision notes

Lines in a circle

The radius goes from centre to edge. The diameter crosses the whole circle through the centre. A chord joins two points on the edge without going through the centre.

A diameter is therefore a special chord — the longest one possible.

Regions of a circle

A sector is a slice bounded by two radii and an arc, like a slice of pizza.

A segment is the region between a chord and the arc, which is what remains when you cut straight across rather than from the centre.

Tangents and arcs

A tangent touches the circle at exactly one point and is perpendicular to the radius there.

An arc is any part of the circumference. Learning these names properly is essential for circle theorem questions later.

Key points

  • The radius runs from centre to edge.
  • The diameter is twice the radius.
  • The circumference is the distance around.
  • A chord joins two points on the edge.
  • A sector is bounded by two radii and an arc.
  • A tangent touches at exactly one point.

Worked examples

Example 1

A circle has radius \(9\)cm. Find its diameter.

Working

\[9 \times 2\]the diameter is twice the radius
\[= 18\text{cm}\]state the diameter

Example 2

Name the line that joins two points on a circle without passing through the centre.

Working

\[\text{Not through the centre}\]this rules out the diameter
\[\text{A chord}\]name the line

Example 3

Name the region bounded by two radii and an arc.

Working

\[\text{Bounded by two radii}\]this describes a slice from the centre
\[\text{A sector}\]name the region

Common mistakes

  • Confusing radius and diameter.

    The diameter is twice the radius, and using the wrong one is the commonest circle error.

  • Mixing up sector and segment.

    A sector is cut from the centre; a segment is cut off by a chord.

  • Calling any line across the circle a diameter.

    It must pass through the centre. Otherwise it is a chord.

  • Confusing a tangent with a chord.

    A tangent touches at one point; a chord cuts across, meeting the circle twice.

Exam tips

  • Learn the names precisely — later topics depend on them.
  • Check whether a question gives the radius or the diameter.
  • Remember a sector comes from the centre, a segment from a chord.
  • Sketch and label the part being described if you are unsure.

Key terms

Radius
The distance from centre to edge.
Chord
A line joining two points on the circle.
Tangent
A line touching the circle at one point.
Segment
The region between a chord and an arc.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.