Lesson G10

G10 Circle theorems and proofs Quiz: AQA Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson G10, Circle theorems and proofs: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 4: Geometry and measures, written with Revision Ninja.

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The 20 questions

  1. (H) The angle at the centre is twice the angle at the circumference subtended by the same arc. If the circumference angle is 35 degrees, what is the centre angle?

    • 145 degrees
    • 35 degrees
    • 70 degrees
    • 140 degrees

  2. (H) What is the angle in a semicircle?

    • 90 degrees
    • 45 degrees
    • 60 degrees
    • 180 degrees

  3. (H) What is true of angles in the same segment of a circle?

    • They are supplementary
    • They are equal
    • They are complementary
    • They are always 90 degrees

  4. (H) Opposite angles in a cyclic quadrilateral add up to what?

    • 360 degrees
    • 180 degrees
    • 120 degrees
    • 90 degrees

  5. (H) The tangent at a point on a circle is perpendicular to which line at that point?

    • The radius
    • The tangent from an external point
    • The diameter through the centre
    • The chord through that point

  6. (H) Two tangents are drawn from an external point. What is true about them?

    • They are twice the radius
    • They are parallel
    • They are equal in length
    • They are perpendicular to each other

  7. (H) A perpendicular from the centre of a circle to a chord does what to the chord?

    • Removes it
    • Makes it a tangent
    • Doubles its length
    • Bisects it

  8. (H) Under the alternate segment theorem, the angle between a tangent and a chord equals what?

    • The angle in the alternate segment
    • An angle of 90 degrees
    • The exterior angle of the chord
    • The angle at the centre

  9. (H) Centre O, arc AB subtends 58 degrees at a point on the circumference. What is angle AOB?

    • 116 degrees
    • 58 degrees
    • 122 degrees
    • 29 degrees

  10. (H) In cyclic quadrilateral ABCD, angle A is 85 degrees. What is angle C?

    • 105 degrees
    • 275 degrees
    • 95 degrees
    • 85 degrees

  11. (H) A tangent and a chord from its point of contact make an angle of 48 degrees. What is the angle in the alternate segment?

    • 42 degrees
    • 132 degrees
    • 96 degrees
    • 48 degrees

  12. (H) Two tangents from point P touch the circle at A and B. PA = 9 cm. What is PB?

    • 9 cm
    • 4.5 cm
    • 18 cm
    • 81 cm

  13. (H) In a cyclic quadrilateral, what does an exterior angle equal?

    • The sum of the interior opposite angles
    • The adjacent interior angle
    • The interior opposite angle
    • 90 degrees

  14. (H) In a semicircle, triangle ABC has AB as a diameter and angle A = 32 degrees. What is angle B?

    • 58 degrees
    • 148 degrees
    • 32 degrees
    • 122 degrees

  15. (H) A perpendicular from the centre bisects a chord of length 24 cm. How long is half the chord?

    • 48 cm
    • 24 cm
    • 6 cm
    • 12 cm

  16. (H) A circle has radius 5 cm and a chord of length 8 cm. How far is the chord from the centre?

    • 4 cm
    • 6 cm
    • 9 cm
    • 3 cm

  17. (H) An angle at the centre is 140 degrees. What is the angle at a point on the major arc subtended by the same arc?

    • 280 degrees
    • 40 degrees
    • 140 degrees
    • 70 degrees

  18. (H) What is true of angles subtended by equal chords at the centre?

    • They are equal
    • They are supplementary
    • They are right angles
    • They double each other

  19. (H) Centre O, chord XY, with angle OXY = 35 degrees. What is angle XOY?

    • 110 degrees
    • 145 degrees
    • 70 degrees
    • 35 degrees

  20. (H) Which proof step uses two radii and a chord to form an isosceles triangle?

    • Angles on a straight line through the centre of the circle
    • Isosceles triangles formed by two radii and a chord
    • Vertically opposite angles at the centre of the circle
    • Alternate angles on parallel lines formed by the chord

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