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0580/42 May/Jun 2022, Question 2: Tangent Properties of a Circle

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 7 marks

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The question, in short

For two circle diagrams, use angle facts to calculate a required angle, justifying each step in part a and showing the method in part b.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 3 marks

Given a circle with diameter PR and angle RPQ = 29°, find angle PSQ, stating a reason for every stage.

  1. 1Angle PQR = 90° (angle in a semicircle)
  2. 2Angle PRQ = 180 − 90 − 29 = 61° (angle sum of triangle = 180°)
  3. 3Angle PSQ = angle PRQ = 61° (angles in the same segment)

AnswerPQR = 90 (angle in a semicircle), PRQ = 61 (angle sum of triangle = 180), PSQ = 61 (angles in the same segment)

Part (b) · 4 marks

With tangent CTS at T, straight line ABC, AB = BT and angle ATS = 98°, calculate angle ACT.

  1. 1Angle ABT = angle ATS = 98° (alternate segment theorem)
  2. 2Triangle ABT is isosceles: angle TAB = angle ATB = (180 − 98) ÷ 2 = 41°
  3. 3Angle TBC = 180 − 98 = 82° (angles on a straight line)
  4. 4Angle BTC = angle TAB = 41° (alternate segment theorem)
  5. 5Angle ACT = 180 − 82 − 41 = 57°

Answer57

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Also searched as: 0580/42/M/J/22 · 0580_s22_qp_42 · 0580 s22 42 · question 2.
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