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      Question

      Length of a chord in a circle of radius 'r' cm, is 16 cm

      and distance between chord and centre of the circle is 15 cm. Find the value of (5r - 19).
      A 62 Correct Answer Incorrect Answer
      B 66 Correct Answer Incorrect Answer
      C 70 Correct Answer Incorrect Answer
      D 74 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 = (16/2) = 8 cm
      By Pythagoras theorem,
      OA 2 = OC 2 + AC 2
      Or, r 2 = 15 2 + 8 2
      Or, r 2 = 225 + 64
      Or, r 2 = 289
      So, 'r' = 17
      But length cannot be negative. So, 'r' = 17
      Required value = 5 X 17 - 19 = 66

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