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Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter

Shape and Space 2

18 practice questions

Start practising (18 questions)

Practice questions

11–18 of 18

  1. Question 11

    3 marks · Normal

    A, B, C, and D lie on a circle with centre O. Angle ABC is 115°.

    Geometry diagram with points O, A, B, C, DOABCD
    Diagram not accurately drawn.
    (a)

    Work out the size of angle CDA.

    [2 marks]
    (b)

    Explain why your answer is correct.

    [1 mark]
    Answer and see the solution →

  2. Question 12

    4 marks · Normal

    The diagram shows a circle with centre O. The radius of the circle is 5 cm. Chord AB is 8 cm long.

    Geometry diagram with points O, A, BOAB
    (a)

    Find the perpendicular distance from O to AB.

    [3 marks]
    (b)

    Explain why this line bisects AB.

    [1 mark]
    Answer and see the solution →

  3. Question 13

    4 marks · Normal

    In the circle below, centre O, angle BAC = 70° and chord BC is a diameter.

    Geometry diagram with points O, A, B, COABC
    (a)

    Calculate angle ABC.

    [2 marks]
    (b)

    Give a reason for your answer.

    [2 marks]
    Answer and see the solution →

  4. Question 14

    4 marks · Normal

    The diagram shows a circle with centre O. PT is a tangent to the circle at P. OP = 7 cm. Work out the length OT if angle OPT = 60°.

    Geometry diagram with points O, P, TOPT
    Circle with tangent and radius.
    (a)

    Find OT.

    [3 marks]
    (b)

    State the property relating the tangent to the radius at P.

    [1 mark]
    Answer and see the solution →

  5. Question 15

    2 marks · Normal

    A square has sides of length 6 cm. Calculate the length of its diagonal to 3 significant figures.

    (a)
    [2 marks]
    Answer and see the solution →

  6. Question 16

    4 marks · Hard

    In the diagram below, ABCD is a cyclic quadrilateral inside a circle with centre O.

    Geometry diagram with points O, A, B, C, DOABCD
    Cyclic quadrilateral with angles marked.

    Angle BAD = 82° and angle BCD = 71°.

    Calculate the size of angle ABC, giving a reason for each step of your working.

    Answer and see the solution →

  7. Question 17

    4 marks · Hard

    The diagram below shows a circle with centre O. The point M is the midpoint of chord AB. AB = 14 cm and OM = 6 cm.

    Geometry diagram with points O, A, B, MOABM
    Circle with OM perpendicular to chord AB.

    Work out the radius of the circle.

    Answer and see the solution →

  8. Question 18

    5 marks · Hard

    The diagram below shows a tangent to the circle with centre O. P is the point of contact, and the radius OP is 8 cm. The tangent TP meets a straight line passing through the centre O at point T, such that angle OTP = 35°.

    Geometry diagram with points O, P, TOPT
    Circle with tangent, radius, and angle marked.
    (a)

    State the relationship between the tangent and the radius at point P.

    [1 mark]
    (b)

    Calculate the length TP. Give your answer to 3 significant figures.

    [4 marks]
    Answer and see the solution →