CAT 2015 Quantitative Ability

Question : 25 of 34

Marks: +1, -0

In the figure, O and O' are the centres of the bigger and smaller circles respectively and small circle touches the square ABCD at the mid point of side AD. The radius of the bigger circle is equal to 15 cm and the side of the square ABCD is 18 cm. Find the radius of the smaller circle.

4.25 cm
4.5 cm
4.75 cm
5 cm

Validate

Solution:

Let the radius of the bigger circle be R and that of the smaller circle be r and the side of the square is 2a.
∴

OE = R - EF

= R - [2R - (2r + 2a)]

OE^2 + EB^2= OB^2

i.e

[ 2a + 2r - R]^2 + a^2 = R^2

a = 9 (∵ 2a = 18); R = 15

∴

(18 + 2r - 15)^2 + 9^2 = 15^2

2r + 3 = 12

∴ r=9/2 = 4.5

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