4MA1/1HR Jan 2019, Question 19: Combining Circle Theorems
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
Circle with tangent AB at B parallel to chord ED; angle ABE = 73°. Find angle DCE, justifying each stage.
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Solution · 5 marks
- 1Angle BCE = 73° (alternate segment theorem)
- 2Angle BDE = 73° (angles in the same segment)
- 3Angle DEB = 73° (alternate angles, AB parallel to ED)
- 4Angle DBE = 180 − 73 − 73 = 34° (angles in a triangle sum to 180°)
- 5Angle DCE = 34° (angles in the same segment)
Answer34
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