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3 marksGeometric Problem Solving (Circles and Circle Theorems)

CSEC Mathematics · May/June 2008 · Paper 2 · Question 12(a)(ii)

This question involves geometry and trigonometry. The figure below, not drawn to scale, shows a cyclic quadrilateral KLMN with KN = KL. PNQ is a tangent to the circle at N and ∠PNK = 24°.

Calculate, stating reasons for your answers, the size of the following angles: NKL.

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Other parts of this question

  1. 12(a)(i)Calculate, stating reasons for your answers, the size of the following angles: KLN.[2 marks]
  2. 12(a)(iii)Calculate, stating reasons for your answers, the size of the following angles: LMN.[2 marks]
  3. 12(b)(i)Copy the diagram and a) label the arc which represents 25°W b) draw an arc to represent the circle of latitude 60°N.[3 marks]
  4. 12(b)(ii)On your diagram, show the points a) R (60°N, 25°W) b) T (60°N, 40°E).[2 marks]
  5. 12(b)(iii)Calculate to the nearest kilometre, the distance from R to T measured along the circle of latitude 60°N.[3 marks]

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