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📐 Mathematics  ·  Circles & Mensuration  ·  JEE

The angle between two chords intersecting inside a circle equals:

Answer: Half the sum of intercepted arcs.

  • A Half the sum of intercepted arcs
  • B Half the difference of intercepted arcs
  • C The sum of intercepted arcs
  • D The central angle

Correct answer: A. Half the sum of intercepted arcs

Explanation: Chords PQ and RS intersect at point X inside the circle. Inscribed angle theorem gives ∠PXR=(arc PR + arc QS)/2. The angle equals half the sum of the two intercepted arcs (near and far). Ans: Half the sum 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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