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4MA1/1HR Jun 2018, Question 16: Chord Properties

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 7 marks

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The question, in short

Using a circle through X, Y, B, C with secants AXY and ABC, AX = 12 cm, XY = AB = x cm, BC = 4 cm, derive a quadratic in x and find AC.

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

Part (a) · 3 marks

Show, using the intersecting secants from A, that x satisfies x² − 8x − 144 = 0.

  1. 1Intersecting lines from A: AX × AY = AB × AC
  2. 212(12 + x) = x(x + 4)
  3. 3144 + 12x = x² + 4x
  4. 4x² − 8x − 144 = 0

Answerx² − 8x − 144 = 0

Part (b) · 4 marks

Solve for x and hence find the length AC, giving the answer to 3 significant figures.

  1. 1x = (8 ± √(64 + 576)) ÷ 2 = (8 ± √640) ÷ 2
  2. 2x = 16.649… (a length cannot be negative)
  3. 3AC = x + 4 = 20.649…
  4. 4AC = 20.6 cm (3 s.f.)

Answer20.6

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