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4024/11 May/Jun 2022, Question 19: Combining Circle Theorems

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Circle with centre O, tangent AC at B, points D, E, F, G on circumference; given angle DFG = 75° and angle ABG = 48°, find three angles.

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Part (a) · 1 mark

Find angle DEG using the given angle DFG = 75°.

  1. 1Angles in the same segment are equal
  2. 2Angle DEG = angle DFG = 75°

Answer75

Part (b) · 1 mark

Find angle DOG at the centre.

  1. 1Angle at centre = 2 × angle at circumference
  2. 2Angle DOG = 2 × 75 = 150°

Answer150

Part (c) · 2 marks

Find angle DBC, using tangent and chord properties.

  1. 1Angle DBG = 180 − 75 = 105° (opposite angles of cyclic quadrilateral DBGF)
  2. 2Angle DBC = 180 − 48 − 105 = 27° (angles on a straight line)

Answer27

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Also searched as: 4024/11/M/J/22 · 4024_s22_qp_11 · 4024 s22 11 · question 19.
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