Position of two circles — A/L Combined Mathematics

How do I practise Position of two circles?

1 question with a worked solution

Check before you answer: Centres and Radii Extraction: Accurately extracting C₁, C₂, r₁, and r₂ from the general circle forms before calculating distance d.

1. Two circles have centers C₁ and C₂ and radii r₁ and r₂, respectively. What is the geometric relationship between the two circles when the distance between their centers d = C₁C₂ satisfies d = r₁ + r₂?
   1. A) The circles touch each other internally
   2. B) The circles touch each other externally at exactly one point
   3. C) The circles intersect each other at two distinct points
   4. D) One circle lies entirely inside the other without touching
   Check my answer

   Correct answer: B) The circles touch each other externally at exactly one point

   When the distance between the centers equals the sum of the radii (d = r₁ + r₂), the two circles meet at a single common point on the line of centers between them, touching each other externally.

   Show worked solution

   Step 1: Check distance between centers d vs (r₁ + r₂). Step 2: d = r₁ + r₂ => Circles touch externally. Answer: The circles touch each other externally at exactly one point.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Position of two circles fit in the syllabus?

Year 1 · Term 3