MathematicsTwo concentric circles are of radius 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Two concentric circles are of radius 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.


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

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    Solution:

    Let C1 be the circle with radius 3 cm and C2 be the circle with radius 5 cm. Let O be the center of the circles.
    Let the chord of C2 that touches C1 be BD. The point of contact as C.
    OC = 3 cm,OB = OD = 5 cm.
    Tangent at any point of a circle is perpendicular to the radius through the point of contact.
    OCBD
    In triangle OBC,
    OB2=OC2+BC2
    52=32+BC2
    BC2=25-9=16
    BC=4 cm
    Also, CD = 4 cm
    BD = BC + CD = 8 cm
    So, Option 2 is correct.
     
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