NTSE Stage 2 SAT 2015 Question Paper

Question : 46 of 100

Marks: +1, -0

A circle with area A

\cm^2

is contained in the interior of a larger circle with area (

\A + \B)\cm^2

and the radius of the larger circle is 4 cm. If A, B, A + B are in arithmetic progression, then the diameter (in cm) of the smaller circle is

Solution:

According to question
∴

2\b=\A+\A+\B

∴

\B=2\A

∴

\B=2\A

∴ Area of bigger circle

\A+\B=3\A

∴

\π\R^2=3\A

∴

\π(4)^2=3\A

∴

\A={16π}/3

Now A is the area of smaller circle
∴

\A=\π\r^2

∴

16/3=\r^2

∴

\r=4/√3={4√3}/3

∴ option (b is correct)

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