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Question

A square is inscribed in a circle with radius 'r'. What is the probability that a randomly selected point within the circle is not within the square?



Solution

The correct option is B


Let the square be ABCD.

Length of the diagonal of the square ABCD = (r + r) = 2r

As ΔBCD is right-angled at C, applying Pythagoras theorem:

(BC)2+(CD)2=(BD)2

a2+a2=(2r)2

2a2=4r2 a=2r

Area (sq ABCD) = 2r2
Area (circle) = π r2

Area (circle) - Area (sq ABCD) =r2(π2)

So, P (that a randomly selected point within the circle is not within the circle)

=(Area(circle)Area(sqABCD))Area(circle) =(r2(π2))π×r2

=(π2)π

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