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(π−2) So, P (that a randomly selected point within the circle is not within the circle) =(Area(circle)−Area(sqABCD))Area(circle) =(r2(π−2))π×r2 =(π−2)π

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