Lemmara logoLemmaraWorked solution

0606/13 May/Jun 2026, Question 9: Circles Meeting Lines, and Tangents

Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 8 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Circle centre (3, 1) radius 1; line 2y + x = c. Find the two c values making the line tangent, then describe the line's position when c lies between them.

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

Part (a) · 7 marks

Find the two possible values of c for which the line 2y + x = c is tangent to the circle.

  1. 1Circle: (x − 3)² + (y − 1)² = 1
  2. 2Substitute x = c − 2y: (c − 2y − 3)² + (y − 1)² = 1
  3. 35y² + y(10 − 4c) + (c² − 6c + 9) = 0
  4. 4Tangent so discriminant = 0: (10 − 4c)² − 20(c² − 6c + 9) = 0
  5. 54c² − 40c + 80 = 0, c² − 10c + 20 = 0
  6. 6c = 5 ± √5

Answerc = 5 ± √5

Part (b) · 1 mark

For c between the two values from part a, state how the line relates to the circle.

  1. 1Between the two tangent values the line passes closer to the centre than the radius
  2. 2So it cuts the circle at two points

AnswerThe line meets (intersects) the circle at two points – it is a chord

Stuck on a step? Read the free lesson: Circles Meeting Lines, and Tangents

Practise more circles meeting lines, and tangents questions

Real 0606 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on circles meeting lines, and tangents

Also searched as: 0606/13/M/J/26 · 0606_s26_qp_13 · 0606 s26 13 · question 9.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.