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Question

In the adjoining figure, ABCD is a rectangle in which length is twice of breadth. H and G divide the line CD into three equal parts. Similarly, points E and F trisect the line AB. A circle PQRS is circumscribed by a square PQRS which passes through the points E, F, G and H. What is the ratio of areas of circles to that of the rectangle?

A
3π:7
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B
3π:4
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C
25π:72
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D
32π:115
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Solution

The correct option is C 25π:72

Let AD = 3a and DC = 6a
DH=HG=GC=6a3=2aHM=MG=2aa=a=SM NQ=a SQ=SM+MN+NQ
= a + 3a + a = 5a
Since diagonal of square SQ = 5a
But, diameter of circle SQ = diagonal of square SQ
Radius of the circle =5a2
Area of the circle =π×(5a2)2
Hence,Area of circleArea of rectangle=254(a2π)3a×6a=25π72

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