CAIE IGCSE Mathematics Core Circle Theorem Questions

Practise applying angle-in-a-semicircle and tangent–radius facts and giving the named circle theorem that justifies each angle result.

Syllabus
2028–2030
Topic
C4.7
Level
Core

Exam points

  • use a diameter to identify a 90° angle at the circumference and state the semicircle theorem
  • use the radius–tangent angle as 90° at the exact point where the tangent touches the circle
  • combine the circle fact with triangle angle sums or isosceles radii to calculate remaining angles

Covered syllabus points

C4.7.1 Calculate unknown angles and give explanations using the following

C4.7 Circle theorems question 1

[Maximum number: 1]

The diagram shows a circle, centre O, radius 11 cm. C, F, G and H are points on the circumference of the circle.
The line AD touches the circle at C and is parallel to the line EG. B is a point on AD and angle ABO=140∘A B O=140^{\circ}.

Give a reason why angle BCO is 90∘90^{\circ}.

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