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      Question

      Length of a chord in a circle of radius 'r' cm, is 14 cm

      and distance between chord and centre of the circle is 24 cm. Find the value of (4r - 60).
      A 36 Correct Answer Incorrect Answer
      B 40 Correct Answer Incorrect Answer
      C 44 Correct Answer Incorrect Answer
      D 48 Correct Answer Incorrect Answer

      Solution

      Image

      AB is the chord of circle.
      Perpendicular line joining the centre of circle and chord, bisects the chord.
      i.e. AC = BC = (14/2) = 7 cm
      By Pythagoras theorem,
      OA 2 = OC 2 + AC 2
      Or, r 2 = 24 2 + 7 2
      Or, r 2 = 576 + 49
      Or, r 2 = 625
      So, 'r' = 25
      But length cannot be negative. So, 'r' = 25
      Required value = 4 X 25 - 60 = 40

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