4MA1/1H Jun 2019, Question 20: Alternate Segment Theorem
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
Cyclic quadrilateral ABCD with tangent TDV at D, AB = AD and angle ADT = 71°. Find angle BCD, justifying each stage.
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Solution · 5 marks
- 1Angle ABD = angle ADT = 71° (alternate segment theorem)
- 2AB = AD, so angle ADB = 71° (base angles of isosceles triangle)
- 3Angle BAD = 180° − 71° − 71° = 38° (angles in a triangle)
- 4Angle BCD = 180° − 38° = 142 (opposite angles of a cyclic quadrilateral)
Answer142
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