GCSE · Circles, arcs & sectors

Parts of a circleExam-style questions

The names of the parts of a circle and how to tell them apart: centre, radius, diameter and circumference; chords, arcs and tangents; sectors and segments, minor and major. Why the diameter is twice the radius, and how two radii make an isosceles triangle.

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13 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4
  1. 1
    Asha has a circular rug with a radius of 8585 cm.

    She wants to lay the rug flat on the floor of a corridor. The corridor is 1.61.6 m wide.

    Will the rug fit across the width of the corridor without being folded?

    Show how you decide.

    (3 marks)
    Level 3 · 3 marksTry it
  2. 2
    Here are four statements about a circle, centre OO.

    For each statement, tick one box.
    StatementTrueMay be trueNot true
    Any two radii of the circle are the same length.
    A chord of the circle passes through OO.
    A segment of the circle has two straight edges.
    A tangent to the circle meets the circle at exactly one point.
    (3 marks)
    Level 3 · 3 marksTry it
  3. 3
    ABAB is a chord of a circle.

    The radius of the circle is 6.56.5 cm.
    (a) Sam assumes that ABAB is a diameter of the circle.

    Using Sam's assumption, work out the length of ABAB.

    (1 mark)
    (b) In fact, ABAB does not pass through the centre of the circle.

    How does the length of ABAB compare with your answer to part (a)?

    Tick one box.
    • ABAB is longer
    • ABAB is the same length
    • ABAB is shorter
    • You cannot tell from the information given
    (1 mark)
    Level 3 · 2 marksTry it
  4. 4
    Here is a circle, centre OO.

    The chord PQPQ divides the circle into two regions. The larger region is shaded.OPQDiagram NOT accurately drawn
    (a) Write down the full mathematical name of the shaded region.

    (1 mark)
    (b) PP and QQ divide the circumference into two arcs.

    Write down the full mathematical name of the arc that forms part of the edge of the shaded region.

    (1 mark)
    Level 3 · 2 marksTry it
  5. 5
    The diagram shows six identical circles inside a rectangle.30 cm20 cmDiagram NOT accurately drawn

    Each circle touches the circles next to it and the sides of the rectangle, as shown.

    The rectangle is 3030 cm long and 2020 cm wide.

    Work out the radius of one of the circles.

    (3 marks)
    Level 3 · 3 marksTry it

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