4MA1/2H Jan 2022, Question 16: Combining Circle Theorems
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 4 marks
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The question, in short
Points D, E, F, G lie on a circle centre O, with EOG a diameter and angle EGD = 42°. Find angle DFG, justifying each step.
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Solution · 4 marks
- 1Angle EGD = 42° (given)
- 2Angle EDG = 90° (angle in a semicircle, since EOG is a diameter)
- 3In triangle EDG, angle DEG = 180° − 90° − 42° = 48°
- 4Angle DFG = angle DEG (angles in the same segment, subtended by the same arc DG)
- 548
Answer48
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