[discia] GCSE Maths › Geometry & Measures › Parts of a Circle

Parts of a Circle

discia.org 10 questions · 16 marks
Name Date
  1. Either paper 1 mark

    Here is a circle with centre \(O\).

    ABCDO

    State the mathematical name of the line \(OA\).

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    radius
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  2. Either paper 1 mark

    A circular clock face on a station wall has a diameter of \(48\) cm.

    O48 cmDiagram NOT accurately drawn

    Work out the radius of the clock face.

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    \(24\ \text{cm}\)
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  3. Either paper 1 mark

    Nadia measures the circular trampoline in her garden. The distance from the centre \(O\) to the edge is \(11\) cm.

    AO11 cmDiagram NOT accurately drawn

    Find the diameter of the trampoline.

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    \(22\ \text{cm}\)
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  4. Either paper 2 marks

    Here is a description of one part of a circle.

    > The part that goes touching the circle at exactly one point.

    Write down its mathematical name, and explain how it differs from a chord.

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    tangent — a chord cuts across and meets the circle twice
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  5. Either paper 3 marks
    Here is a circle with centre \(C\). \(W\), \(X\) and \(Y\) are points on the circle. \(WY\) is a straight line. WXYC Tick one box for each statement.
    TrueFalse
    \(WY\) is a diameter.
    \(WX\) is a chord.
    The shaded section is a sector.
    Arc \(XY\) is part of the circumference.
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    WY is a diameter: True; WX is a chord: True; the shaded section is a sector: True; arc XY is part of the circumference: True
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  6. Either paper 1 mark

    Which of these parts of a circle is a curve?

    Circle your answer.

    diameter     centre     arc     radius

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    arc
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  7. Either paper 1 mark
    Isla adds labels to this diagram of a circle with centre \(O\). ABCDEFO
    LineIsla's label
    \(AB\)diameter
    \(OC\)chord
    \(DE\)chord
    the line touching the circle at \(F\)tangent
    Explain why one of the labels is wrong.
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    The line \(OC\) is labelled "chord" but it starts at the centre O; a chord has both ends on the circumference.
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  8. Either paper 2 marks

    Here is a circle with centre \(O\). The shaded region is bounded by two radii and the arc between them.

    O135°

    The angle at the centre is \(135^\circ\).

    What fraction of the whole circle is shaded? Give your answer in its simplest form.

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    \(\frac{3}{8}\)
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  9. Either paper 3 marks

    \(A\) and \(B\) are points on a circle with centre \(C\).

    ABC

    \(B\) could be in any other position on the circle that still makes a triangle \(ABC\). For each statement, tick one box: definitely true, might be true or cannot be true.

    (a)

    Triangle ABC is equilateral.

    (b)

    AB is longer than the radius of the circle.

    (c)

    Triangle ABC has a right angle.

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    (a) Might be true
    (b) Might be true
    (c) Might be true
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  10. Either paper 1 mark

    An arc is drawn on a circle. Which statement is correct?

    Tick one box.

    ☐ The arc must be longer than the radius.

    ☐ The arc must be equal in length to the radius.

    ☐ The arc must be shorter than the radius.

    ☐ The arc could be longer than, equal in length to or shorter than the radius.

    Show answer
    The arc could be longer than, equal in length to or shorter than the radius.
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discia.org Parts of a Circle · sheet 1
Answers Parts of a Circle · sheet 1
  1. radius
  2. \(24\ \text{cm}\)
  3. \(22\ \text{cm}\)
  4. tangent — a chord cuts across and meets the circle twice
  5. WY is a diameter: True; WX is a chord: True; the shaded section is a sector: True; arc XY is part of the circumference: True
  6. arc
  7. The line \(OC\) is labelled "chord" but it starts at the centre O; a chord has both ends on the circumference.
  8. \(\frac{3}{8}\)
  9. (a) Might be true
    (b) Might be true
    (c) Might be true
  10. The arc could be longer than, equal in length to or shorter than the radius.
discia.org Parts of a Circle · sheet 1