MathematicsAt point A on a diameter AB of a circle of radius 10 cm  , tangent  X A Y  is drawn to the circle. The length of the chord CD parallel to XY at a distance 16 cm   from A is 

At point A on a diameter AB of a circle of radius 10 cm  , tangent  X A Y  is drawn to the circle. The length of the chord CD parallel to XY at a distance 16 cm   from A is


 active attachment

  1. A
         8 cm  
  2. B
         10 cm  
  3. C
         16 cm  
  4. D
         18 cm   

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    Solution:

    Given that radius of the circle is 10cm and tangent XAY is drawn to the circle.
    active attachmentIn right angled triangle, ΔOBC   By Pythagoras theorem,
      O C 2 =O B 2 +B C 2   10 2 = 6 2 +B C 2   100=36+B C 2 B C 2 =64 BC=8cm  
    The length of the chord CD is given as follows:
    CD=2×BC CD=2×8 CD=16 cm  
    Hence, the length of chord CD is 16cm.
    Therefore, option 3 is correct.
     
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