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📐 Mathematics  ·  Circles & Mensuration  ·  JEE

The common external tangents to two circles with radii r₁, r₂ and distance d between centres:

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).

Cylinder, Cone, SphereV=πr²hCSA=2πrhV=⅓πr²hCSA=πrlV=4/3πr³SA=4πr²

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

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