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. What is the relationship between angles in the same segment of a circle?

    • They sum to 180°
    • They are equal
    • They sum to 360°
    • One is double

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

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

  5. A tangent to a circle is perpendicular to which line at the point of contact?

    • Radius
    • Secant
    • Arc
    • Chord

  6. What is true about the lengths of two tangents drawn to a circle from the same external point?

    • They are perpendicular
    • One is double
    • They are equal
    • They sum to 180°

  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. Under the alternate segment theorem, what does the angle between a tangent and chord equal?

    • Alternate segment angle
    • Angle at centre
    • Angle in semicircle
    • Opposite interior angle

  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. What does an exterior angle of a cyclic quadrilateral equal?

    • Angle at centre
    • Interior adjacent angle
    • Interior opposite angle
    • Exterior opposite angle

  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. What is true about angles subtended at the centre by equal chords?

    • They are equal
    • Sum to 360°
    • One is double
    • Sum to 180°

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

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

  20. What shape is formed by two radii and a chord in a circle?

    • Scalene triangle
    • Isosceles triangle
    • Equilateral triangle
    • Right-angled triangle

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