MathematicsTwo concentric circles are of radii 10 cm and 8 cm, then find the length of the chord of the larger circle which touches the smaller circle.

Two concentric circles are of radii 10 cm and 8 cm, then find the length of the chord of the larger circle which touches the smaller circle.


  1. A
    6 cm  
  2. B
    12 cm  
  3. C
    18 cm  
  4. D
    9 cm   

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    Solution:

    Given,
    Two concentric circles are of radii 10 cm and 8 cm.
    We can clearly see that,
    AP=PB   as OP⊥AB   ( The radius of the circle is always perpendicular to the tangent of the circle).
    Applying Pythagoras theorem in ΔOPA   ,
    OA2=OP2+AP2 
    ⇒100=64+AP2
    ⇒AP2=36
    ⇒AP=6cm
    ⇒AB=2AP
    ⇒AB=2×6
    ⇒AB=12cm
    Hence, the length of the chord of the larger circle which touches the smaller circle is 12cm.
    Therefore, the correct option is 2.
     
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