0580/21 Oct/Nov 2023, Question 17: Tangent Properties of a Circle
Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 3 marks
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The question, in short
Use the circle with centre O, tangent DE at C, angle BCE = 53° and angle ACO = 20° to find the value of x, the angle at B between BA and BO.
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Solution · 3 marks
- 1Angle OCE = 90° (radius ⟂ tangent), so angle OCB = 90 − 53 = 37°; OB = OC so angle OBC = 37°
- 2Angle BAC = 53° (alternate segment theorem)
- 3Angle ACB = 20 + 37 = 57°, so angle ABC = 180 − 53 − 57 = 70°
- 4x = 70 − 37 = 33
Answer33
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Also searched as: 0580/21/O/N/23 · 0580_w23_qp_21 · 0580 w23 21 · question 17.
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