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0606/13 May/Jun 2025, Question 5: Circles Meeting Lines, and Tangents

Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 6 marks

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The question, in short

Circle C has equation (x − 5)² + (y − 12)² = 100. Find the tangent at (11, 4) as ax + by = c, and show C misses x² + y² = 4. No accurate drawing allowed.

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

Part (a) · 4 marks

Find the tangent to C at (11, 4), giving it as ax + by = c with integer coefficients a, b, c.

  1. 1Centre (5, 12)
  2. 2Gradient of radius = (12 − 4)/(5 − 11) = −4/3
  3. 3Gradient of tangent = 3/4
  4. 4y − 4 = (3/4)(x − 11)
  5. 54y − 16 = 3x − 33, so 3x − 4y = 17

Answer3x − 4y = 17

Part (b) · 2 marks

Show that circle C and the circle x² + y² = 4 do not intersect.

  1. 1Centres (5, 12) and (0, 0); radii 10 and 2
  2. 2Distance between centres = √(5² + 12²) = 13
  3. 3Sum of radii = 10 + 2 = 12
  4. 413 > 12, so the circles do not intersect

AnswerDistance between centres = 13 > sum of radii = 12, so the circles do not intersect (shown)

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Also searched as: 0606/13/M/J/25 · 0606_s25_qp_13 · 0606 s25 13 · question 5.
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