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CAIE IGCSE Additional Math 8.4 circle-circle intersection problems

Use this circle-intersection page to compare centres and radii, use intersection information and prove touching when required.

Syllabus
2028–2030
Course
Additional Mathematics 0606

Exam points

  • Compare distance between centres with radii to show when two circles touch.
  • Use shared-radius or positive-centre information to form circle equations or intersections.

8.4. Solve circle-circle intersection problems question 1

[Maximum number: 1]

Solutions to this question by accurate drawing will not be accepted.
A circle has equation x2+y2−16x−10y+73=0x^{2}+y^{2}-16 x-10 y+73=0.

A different circle has equation (x−10)2+(y−6.5)2=2.25(x-10)^{2}+(y-6.5)^{2}=2.25.

Show that the two circles touch. You are not required to find the coordinates of the common point.

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