4MA1/2H Nov 2021, Question 11: Combining Circle Theorems
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 3 marks
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The question, in short
Circle with centre O, tangent ABC at B, straight line ODC, diameter BOE, angle BCD = 48°. Find angle DFE.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 3 marks
- 1Tangent meets radius at 90°, so angle OBC = 90°
- 2Angle BOC = 180 − 90 − 48 = 42°
- 3BOE is straight, so angle DOE = 180 − 42 = 138°
- 4Angle at circumference is half the angle at centre: DFE = 138 ÷ 2 = 69°
Answer69
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