3 marksGeometric Problem Solving (Circles and Circle Theorems)

CSEC Mathematics · January 2011 · Paper 2 · Question 10(a)(ii)

A diagram shows a circle with centre O. SGH is a tangent to the circle. ∠FOG = 118° and ∠DGS = 65°.

Calculate, giving reasons for EACH step of your answer, the measure of ∠DEF.

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Other parts of this question

10(a)(i)Calculate, giving reasons for EACH step of your answer, the measure of ∠OGF.[2 marks]
10(b)(i)a)Draw a clearly labelled diagram to represent the above information. Show on the diagram the north/south direction.[3 marks]
10(b)(i)b)Draw a clearly labelled diagram to represent the above information. Show on the diagram the bearing 054°.[1 mark]
10(b)(i)c)Draw a clearly labelled diagram to represent the above information. Show on the diagram the distances 122 km and 60 km.[1 mark]
10(b)(ii)a)Calculate the measure of angle JKL.[7 marks]
10(b)(ii)b)Calculate the distance JL.[1 mark]
10(b)(ii)c)Calculate the bearing of J from L.[1 mark]

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