MathematicsWhat is the length of a chord which is at a distance of 4 cm from the centre of the circle of radius 6 cm?

What is the length of a chord which is at a distance of 4 cm from the centre of the circle of radius 6 cm?


  1. A
    5 cm
  2. B
    6 cm
  3. C
    7cm
  4. D
    8cm 

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    Solution:

    It is given that the radius of the circle is 6cm and distance of chord from the centre is 4cm.
      Let radius OA=6cm and OC=4cm.
    So, seg AC = seg CB     ….(Perpendicular from the center to the chord bisects the chord)
    In right triangle AOC,
    By Pythagoras theorem,
    AC 2 +OC 2 =OA 2 AC 2 +42=52 AC 2 +16=25 AC 2 =9 AC=3cm   But seg AC = seg CB = 3 cm.
    Seg AB = seg AC + seg CB      …. {From figure}
    AB = 3 cm + 3 cm
     AB = 6 cm.
    Therefore, the correct option is (2).
     
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