0580/22 May/Jun 2026, Question 15: Combining Circle Theorems
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 5 marks
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The question, in short
Using a circle through A, B, C, D with tangent EF at A, angle ADB = 20° and angle BCD = 75°, work out angle EAD, justifying each step.
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Solution · 5 marks
- 1Angle BAD = 180° − 75° = 105° (opposite angles of a cyclic quadrilateral sum to 180°)
- 2Angle ABD = 180° − 105° − 20° = 55° (angles in a triangle sum to 180°)
- 3Angle EAD = angle ABD = 55° (alternate segment theorem)
AnswerAngle EAD = 55°. Reasons: opposite angles of a cyclic quadrilateral sum to 180°; alternate segment theorem
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Also searched as: 0580/22/M/J/26 · 0580_s26_qp_22 · 0580 s26 22 · question 15.
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