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Circle theorems

10th grade (Year 11 in England) · 16 questions · Common Core: HSG.C.A.2, HSG.C.A.3 · England: GCSE Higher Geometry

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  1. Question 1

    A triangle is drawn in a semicircle with one side the diameter. One of the other angles is 25°. What is the third angle (not the right angle)?

    Answer

  2. Question 2

    Two angles at the circumference stand on the same arc. One is 50°. What is the other?

    Answer

  3. Question 3

    The angle at the circumference is 57°, standing on the same arc as the angle at the centre. What is the angle at the centre?

    Answer

  4. Question 4

    Two angles at the circumference stand on the same arc. One is 51°. What is the other?

    Answer

  5. Question 5

    A tangent meets a radius at the point of contact. A triangle formed with the centre has an angle of 80° at the centre. What is the angle between the tangent and the line to the centre (the third angle)?

    Answer

  6. Question 6

    Two angles at the circumference stand on the same arc. One is 34°. What is the other?

    Answer

  7. Question 7

    A triangle is drawn in a semicircle with one side the diameter. One of the other angles is 37°. What is the third angle (not the right angle)?

    Answer

  8. Question 8

    Two angles at the circumference stand on the same arc. One is 30°. What is the other?

    Answer

  9. Question 9

    A tangent meets a radius at the point of contact. A triangle formed with the centre has an angle of 65° at the centre. What is the angle between the tangent and the line to the centre (the third angle)?

    Answer

  10. Question 10

    Two angles at the circumference stand on the same arc. One is 25°. What is the other?

    Answer

  11. Question 11

    A tangent meets a radius at the point of contact. A triangle formed with the centre has an angle of 39° at the centre. What is the angle between the tangent and the line to the centre (the third angle)?

    Answer

  12. Question 12

    Two angles at the circumference stand on the same arc. One is 62°. What is the other?

    Answer

  13. Question 13

    A tangent meets a radius at the point of contact. A triangle formed with the centre has an angle of 58° at the centre. What is the angle between the tangent and the line to the centre (the third angle)?

    Answer

  14. Question 14

    Two angles at the circumference stand on the same arc. One is 60°. What is the other?

    Answer

  15. Question 15

    The angle at the circumference is 24°, standing on the same arc as the angle at the centre. What is the angle at the centre?

    Answer

  16. Question 16

    Two angles at the circumference stand on the same arc. One is 28°. What is the other?

    Answer

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  1. 65
  2. 50
  3. 114
  4. 51
  5. 10
  6. 34
  7. 53
  8. 30
  9. 25
  10. 25
  11. 51
  12. 62
  13. 32
  14. 60
  15. 48
  16. 28