0606/22 May/Jun 2026, Question 11: Two Circles
Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 9 marks
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The question, in short
Given circle C₁ centre (3, 5) with P(1, 4) on it, and circle C₂ centre (12, 8) sharing chord y = 19 − 3x, find the radius of C₂ without accurate drawing.
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Solution · 9 marks
- 1r₁² = (1 − 3)² + (4 − 5)² = 5, so C₁: (x − 3)² + (y − 5)² = 5
- 2Substitute y = 19 − 3x: (x − 3)² + (19 − 3x − 5)² = 5
- 310x² − 90x + 200 = 0, so x² − 9x + 20 = 0
- 4x = 4 or x = 5: intersection points (4, 7) and (5, 4)
- 5r₂² = (12 − 5)² + (8 − 4)² = 49 + 16 = 65
- 6Radius of C₂ = √65
Answer√65
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Also searched as: 0606/22/M/J/26 · 0606_s26_qp_22 · 0606 s26 22 · question 11.
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