0580/22 Feb/Mar 2021, Question 15: Combining Circle Theorems
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 2 marks
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The question, in short
In a circle with equal chords EG and EH, tangent ET at E, and chords HF and EG crossing at K, use angle FET = 47° and angle FEG = 25° to find x, where angle HEG = x°.
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Solution · 2 marks
- 1Angle EHF = angle FET = 47° (alternate segment theorem)
- 2Angle GHF = angle GEF = 25° (angles in the same segment)
- 3Angle EHG = 47 + 25 = 72°
- 4EG = EH so angle EGH = angle EHG = 72°
- 5x = 180 − 72 − 72 = 36
Answer36
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