Answer: 2 (if circles do not overlap externally).
- A 2, counted without checking whether the circles intersect
- B d/|r₁-r₂|, a ratio mistaken for a count of tangents
- C 2 (if circles do not overlap externally)
- D Depends on d, since the count is assumed to vary continuously with it
Correct answer: C. 2 (if circles do not overlap externally)
Explanation: Two external tangents exist when circles are separate (d > r₁+r₂) or d = r₁+r₂ (externally tangent, 1 common external point).
Three standard 3D solids and their key formulas: a cylinder's volume scales with the full height, a cone's volume is exactly one-third of the cylinder with the same base and height, and a sphere's volume and surface area both follow distinct r-based formulas worth memorising separately.
Concept context
Perimeters, areas, and volumes of 2D and 3D shapes