Question
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? 
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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:
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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