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Grade 11 · Euclidean Geometry
Circle Geometry: The Theorems, With Examples
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  / 15

Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    Arc subtends 120° at the centre. Angle at the circumference? (centre/circ)
    (2)
    ABP 120° ? O is the centre
  2. 2
    Angle at the circumference is 35°. Angle at the centre (same arc)? (centre/circ)
    (2)
    ABP ? 35° O is the centre
  3. 3
    AB is a diameter, P on the circle. What is AP̂B? (semicircle)
    (1)
    ABP ? AB is a diameter
  4. 4
    In a semicircle, PÂB = 40°. Find AB̂P. (semicircle)
    (2)
    ABP ? 40° AB is a diameter
  5. 5
    Cyclic quad angle is 110°. Opposite angle? (cyclic quad)
    (1)
    ABCD 110° ? ABCD is a cyclic quadrilateral
  6. 6
    Cyclic quad angle is 75°. Opposite angle? (cyclic quad)
    (1)
    ABCD 75° ? ABCD is a cyclic quadrilateral
  7. 7
    Two angles stand on the same arc; one is 52°. The other? (same segment)
    (1)
    52°xABPQ
  8. 8
    Tangent–chord angle is 70°. Angle in the alternate segment? (tan–chord)
    (2)
    TAB?70°
  9. 9
    A tangent meets a radius at the point of contact. What is the angle? (tan–radius)
    (1)
    OT
  10. 10
    Angle at centre = 2x and equals 100°. Find x, the angle at the circumference. (solve)
    (2)
    ABP 100° x O is the centre
TOTAL: 15 marks
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