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2 marksGeometric Problem Solving (Circles and Circle Theorems)

CSEC Mathematics · Question 10(a)(iv)

The diagram below, not drawn to scale, shows a circle with centre O. The points A, B, C and D are on the circumference of the circle. EAF and EDG are tangents to the circle at A and D respectively. AÔD = 114° and CDG = 18°.

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

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Other parts of this question

  1. 10(a)(i)Calculate, giving reasons for EACH step of your answer, the measure of ∠ACD.[2 marks]
  2. 10(a)(ii)Calculate, giving reasons for EACH step of your answer, the measure of ∠AED.[2 marks]
  3. 10(a)(iii)Calculate, giving reasons for EACH step of your answer, the measure of ∠OAC.[2 marks]
  4. 10(b)(i)A straight adjustable wire connects R to P along the top of the cuboid. Calculate the length of the wire RP.[1 mark]
  5. 10(b)(ii)The connection at P is now adjusted and moved to T. Calculate the length of the wire RT.[2 marks]
  6. 10(b)(iii)Calculate the angle TRV.[2 marks]
  7. 10(b)(iv)Complete the following statements: The size of the angle through which the wire moves from RP to RT is _____. An angle which is the same in size as RTV is…[2 marks]

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