0580/22 May/Jun 2023, Question 13: 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 points A, B, C, D, AB parallel to DC, angle ACD = 32°, chords AC and DB meet at E; find x, the marked angle AEB.
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Solution · 2 marks
- 1Angle CAB = angle ACD = 32° (alternate angles, AB ∥ DC)
- 2Angle ABD = angle ACD = 32° (angles in the same segment)
- 3x = 180 − 32 − 32 = 116 (angles in triangle ABE)
Answer116
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