0580/22 May/Jun 2021, Question 13: Combining Circle Theorems
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 3 marks
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The question, in short
A circle with centre O has points A, B, C on it and tangents DA, DC meeting at D with angle ADC = 44°. Find x, the size of angle ABC.
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Solution · 3 marks
- 1Tangent meets radius at 90°, so angle OAD = angle OCD = 90°
- 2Angle AOC = 360 − 90 − 90 − 44 = 136°
- 3Angle at the centre is twice the angle at the circumference
- 4x = 136 ÷ 2 = 68
Answer68
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