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📐 Mathematics  ·  Circles & Mensuration  ·  JEE

The length of the tangent from (5, 3) to the circle x² + y² − 2x − 4y − 4 = 0 is:

Answer: 2√2.

  • A 2√2
  • B 4
  • C 2√3
  • D 3

Correct answer: A. 2√2

Explanation: Tangent length = √(S₁) = √(25 + 9 − 10 − 12 − 4) = √8 = 2√2.

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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