Question 187055
One has a circle inscribed in a square(round peg in square hole). The other has a square inscribed in a circle.(square peg in round hole)How do I determine which one is the better fit? Is there some method to this madness????
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The better fit is the one where the inner figure fills more of the
area of the outer figure.
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If the circle is inside the square:
Area of the square = s^2
Area of the circle = (pi)(s/2)^2 = (1/4)pi*s^2 = 0.7854*s^2
The area of the square that remains is (1-0.7854)s^2 = 0.2146s^2

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If the square is inside the circle:
Comment:
Now you need to know if the two circles are of the same size
of if the two squares are of the same size, because you need
to relate the two figures.
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Cheers,
Stan H.