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📐 Mathematics  ·  Circles & Mensuration  ·  JEE

The angle between a tangent to a circle and a secant from the same external point:

Answer: Half the difference of intercepted arcs.

  • A Half the difference of intercepted arcs
  • B Half the sum of intercepted arcs
  • C Equals the central angle
  • D 90°

Correct answer: A. Half the difference of intercepted arcs

Explanation: From external point, tangent touches at T (arc=0 from near side), secant cuts arcs m (near) and n (far). Angle=(n−m)/2 = half the difference of intercepted arcs. For tangent-secant, near arc is the tangent-point arc. Ans: Half the difference of intercepted arcs.

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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