0580/23 Oct/Nov 2025, Question 13: Combining Circle Theorems
Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 4 marks
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The question, in short
Circle centre O with points A, B, C, D on circumference; tangents ED and EB; AC parallel EB; angle AOD = 44°. Find x, where angle OEB = x°.
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Solution · 4 marks
- 1Angle OBE = angle ODE = 90° (tangent meets radius at 90°)
- 2OE bisects angle DEB, so angle OED = x
- 3AC is parallel to EB, so angle AOE = angle OEB = x (alternate angles), and angle DOE = 44 + x
- 4Triangle ODE: x + x + 44 + 90 = 180
- 52x = 46, x = 23
Answer23
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