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4MA1/2F Jun 2018, Question 9: Tangent Properties of a Circle

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2F (Foundation) · Calculator · 5 marks

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The question, in short

For a circle with centre O and points R, S on it, identify a segment and name line RS; then with angle OPQ = 18° and tangent QT at Q, find angle PQT with reasons.

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

Part (a) · 1 mark

Shade on the given circle diagram the region that is a segment.

  1. 1Shade the region bounded by the chord RS and the arc RS.

AnswerSegment shaded

Part (b) · 1 mark

State the mathematical term for the straight line joining R and S.

  1. 1The straight line RS connects two points on the circle without passing through the centre.
  2. 2This is called a chord.

AnswerChord

Part (c) · 3 marks

Using OPQ = 18° and tangent QT at Q, calculate angle PQT, justifying each step.

  1. 1QT is a tangent and OQ is a radius, so angle OQT = 90° (the angle between a tangent and a radius is 90°)
  2. 2OP = OQ because both are radii, so triangle OPQ is isosceles
  3. 3So angle OQP = angle OPQ = 18° (base angles of an isosceles triangle are equal)
  4. 4Angle PQT = angle OQT − angle OQP
  5. 5Angle PQT = 90° − 18° = 72°

Answer72

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