G10 apply and prove the standard circle theorems concerning angles, radii, tangents and... Quiz: Pearson Edexcel Maths, Unit 4

The 20 questions

1. The angle at the centre subtended by an arc is ___ the angle at the circumference subtended by the same arc.

   • equal to
   • three times
   • half
   • twice

2. The angle in a semicircle is:

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

3. Angles subtended by the same arc at points on the circumference are:

   • unrelated
   • twice as large
   • equal
   • supplementary

4. Opposite angles of a cyclic quadrilateral add up to:

   • 180 degrees
   • 360 degrees
   • 90 degrees
   • 270 degrees

5. Tangents drawn from an external point to a circle are:

   • twice the radius
   • equal in length
   • parallel
   • perpendicular

6. According to the alternate segment theorem, the angle between a tangent and a chord equals what?

   • centre angle
   • alternate segment angle
   • right angle
   • adjacent angle

7. The radius and the tangent at their point of contact meet at:

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

8. A quadrilateral with all four vertices on a circle is called:

   • a kite
   • tangential
   • cyclic
   • a parallelogram

9. The angle at the centre of a circle is 130°. What is the angle at the circumference on the same arc?

   • 65°
   • 50°
   • 260°
   • 130°

10. In cyclic quadrilateral ABCD, angle A is 80°. What is angle C?

    • 100°
    • 10°
    • 280°
    • 80°

11. Points A, B and C lie on a circle, and AB is a diameter. Angle BAC is 35°. What is angle ABC?

    • 90°
    • 35°
    • 145°
    • 55°

12. A tangent PT of length 12 cm is drawn from P, where OP = 13 cm and O is the centre. What is the radius?

    • 12 cm
    • 25 cm
    • 1 cm
    • 5 cm

13. Two tangents from an external point P make a 50° angle at P. What is the angle at the centre between the two radii?

    • 25°
    • 50°
    • 130°
    • 100°

14. The angle between a tangent and a chord is 58°. What is the angle in the alternate segment?

    • 32°
    • 58°
    • 122°
    • 116°

15. Opposite angles of a cyclic quadrilateral are (x + 20)° and (2x − 20)°. What is the size of the angle (x + 20)°?

    • 60°
    • 80°
    • 100°
    • 40°

16. The angle at the centre is 4x and the angle at the circumference on the same arc is x + 30. What is x?

    • 15
    • 30
    • 20
    • 60

17. The minor arc AB subtends 118° at the centre. What is the angle at the circumference subtended by AB from the major arc?

    • 59°
    • 118°
    • 62°
    • 121°

18. In a cyclic quadrilateral, what does any exterior angle equal?

    • sum of angles
    • adjacent angle
    • half the angle
    • interior opposite angle

19. The angle AOB at the centre is 84°. What is the angle at the circumference from the major arc side?

    • 96°
    • 138°
    • 42°
    • 84°

20. A cyclic quadrilateral has one angle of 72°. What is the angle opposite it?

    • 108°
    • 18°
    • 288°
    • 72°

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