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2 marksGeometric Problem Solving (Circles and Circle Theorems)

CSEC Mathematics · Question 9(a)(i)

A circle has points P, Q, R, T and V on its circumference. QRS is a straight line. Angle PVR = 75° and angle TRS = 60°.

Determine the value of Angle PTR. Show detailed working where necessary and give a reason to support your answer.

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Other parts of this question

  1. 9(a)(ii)Determine the value of Angle TPQ. Show detailed working where necessary and give a reason to support your answer.[2 marks]
  2. 9(a)(iii)Determine the value of Obtuse angle POR where O is the centre of the circle. Show detailed working where necessary and give a reason to support your answer.[2 marks]
  3. 9(b)(i)Complete the diagram below by inserting the angles of depression and the distance between the ships.[1 mark]
  4. 9(b)(ii)a)Determine, to the nearest metre, the distance, TS₂, between the top of the lighthouse and Ship 2.[3 marks]
  5. 9(b)(ii)b)Determine, to the nearest metre, the height of the lighthouse, TB.[2 marks]

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