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In the figure given below, the two circles touch externally. AB is a diameter of the larger circle and C is the centre of the smaller circle. If triangle ABC has an area of 289 sq. cm, then which of the following can be the length of the line segment CD? In The Figure Given Below, The Two Circles Touch Externally....  


Options:
A .   26 cm
B .   28 cm
C .   30 cm
D .   None of these
E .   none of these
Answer: Option D
:
D

Option (d)   
Let the radii of the larger and smaller circles be ‘R’ cm and ‘r’ cm.


Area of triangle ABC =12* AB * OC = 12 * 2R * (R + r) = R * (r + R) = 289


CD = 2R + r, Using AM>GM,  2R + r > = 2 (R (R + r))1/2 = 2 (289)1/2 = 34 cm


So, minimum length = 34 cm.



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