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3 marksGeometric Problem Solving (Circles and Circle Theorems)

CSEC Mathematics · January 2013 · Paper 2 · Question 10(a)(iii)

The diagram shows a circle, centre O. RQ is a diameter and PM and PN are tangents to the circle. Angle MPN = 54° and angle RQM = 20°.

Calculate, giving reasons for your answer, the measure of ∠ PMN.

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Other parts of this question

  1. 10(a)(i)Calculate, giving reasons for your answer, the measure of ∠ MRQ.[2 marks]
  2. 10(a)(ii)Calculate, giving reasons for your answer, the measure of ∠ PMR.[2 marks]
  3. 10(b)(i)a)Calculate the measure of angle ABC.[2 marks]
  4. 10(b)(i)b)Calculate the area of triangle ABC.[2 marks]
  5. 10(b)(ii)a)In your answer booklet, draw the triangle TAB showing the angle of elevation.[2 marks]
  6. 10(b)(ii)b)Calculate the height, TA, of the lighthouse.[2 marks]

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