4MA1/2H Jan 2019, Question 20: Combining Circle Theorems
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks
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The question, in short
In a circle with points A, B, C, D, tangent PCQ at C, AB = CB and angle BCQ = x°, prove angle CDA = 2x°, justifying each step.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1Angle BAC = x (alternate segment theorem)
- 2AB = CB, so angle BCA = angle BAC = x (isosceles triangle)
- 3Angle ABC = 180° − 2x (angles in a triangle add to 180°)
- 4Angle CDA = 180° − (180° − 2x) (opposite angles of a cyclic quadrilateral add to 180°)
- 5So angle CDA = 2x°
Answerproof with reasons
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