4MA1/1HR Jun 2020, Question 15: Combining Circle Theorems
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks
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The question, in short
Using a circle with tangent ABC at B, angle EDF = 40° and angle FBC = 70°, prove that tangent ABC is parallel to chord EF, justifying each step.
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Solution · 4 marks
- 1Angle BDF = 70°, because the angle between a tangent and a chord equals the angle in the alternate segment.
- 2Angle BDE = 70° + 40° = 110°.
- 3Angle BFE = 180° − 110° = 70°, because opposite angles of cyclic quadrilateral BDEF add to 180°.
- 4Angle FBC = angle BFE = 70°; these are alternate angles, so EF is parallel to ABC.
AnswerEF is parallel to ABC
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