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4MA1/2H Jan 2021, Question 13: Combining Circle Theorems

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 3 marks

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The question, in short

On a circle centred O, QOS is a diameter, angle POS is 124°, angle PRS is m° and angle PTS is n°. Work out m, n and angle QPO.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 1 mark

Work out the size of angle PRS, labelled m, using the circle geometry from the diagram.

  1. 1Angle at centre is twice angle at circumference
  2. 2124° ÷ 2 = 62

Answer62

Part (aii) · 1 mark

Work out the size of angle PTS, labelled n, using the circle geometry from the diagram.

  1. 1Opposite angles in a cyclic quadrilateral sum to 180°
  2. 2180 − 62 = 118

Answer118

Part (b) · 1 mark

Work out the size of angle QPO.

  1. 1Triangle QPO: OQ = OP (radii), so isosceles
  2. 2Angle at O: 180 − 124 = 56
  3. 3Base angles equal: (180 − 56) ÷ 2 = 62

Answer62

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