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BITSAT2015MathematicsCircleActual

Area of the circle in which a chord of length 2 makes an angle / 2 at the centre, is

Options

  1. A/ 2 sq units
  2. B2 sq units
  3. Csq units
  4. D/ 4 sq units

Correct answer

C. sq units

Step-by-step solution

Let AB be the chord of length 2 . Let O be the centre of the circle and let O C be the perpendicular from O on AB . Then , AC = BC = 2 2 = 1 2 In OBC , we have aligned OB &= BC cosec 45^ &= 1 2 2 =1 aligned Area of the circle = ( OB )²= sq units

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