Xavier Aptitude Test 2011 Paper

Question : 31 of 101

Marks: +1, -0

Consider a square ABCD of side 60 cm. It contains arcs BD and AC drawn with centres at A and D respectively. A circle is drawn such that it is tangent to side AB and the arcs BD and AC. What is the radius of the circle?

9 cm
10 cm
12 cm
15 cm
None of the above

Validate

Solution:

(b) Let the side of the square be

=1

unit.
Radius of the circle

=\ {OR}=x

.
Also

\ {AO}=\ {AP}-\ {OP}=1-x

\ {DO}= {DQ}+\ {OQ}=1+x

\ {OS}=1-x

\∴\ (1-x)^{2}-x^{2}=(1+x)^{2}-(1-x)^{2}

⇒ 1=6 x ⇒x=\ {1}/{6}

{AB}=60,

=\ {1}/{6}(60)=10

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