CAIE IGCSE Mathematics Core C4.7.1 Calculate unknown angles & give explanations using the following

Practise calculating angles in circle diagrams and explaining each step using diameter, tangent and triangle relationships.

Syllabus
2028–2030
Objective
C4.7.1
Level
Core

Exam points

  • use angle in a semicircle = 90° to calculate a missing angle from a diameter
  • apply tangent-radius perpendicularity when a tangent touches the circle at a point
  • combine circle facts with the angle sum of a triangle to find x or y

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