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A circle is inscribed in a quadrant of a larger circle. Find the ratio of the area of the small circle to that of the quadrant.
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\n" ); document.write( "The larger circle has a radius R.
\n" ); document.write( "This circle about the Origin is x^2 + y^2 = R^2
\n" ); document.write( "The smaller circle has radius r. Its center will be on the line x = y in the 1st quadrant.
\n" ); document.write( "The smaller circle's eqn is (x-h)^2 + (y-h)^2 = r^2
\n" ); document.write( "R = r(1 + sqrt(2))
\n" ); document.write( "The area is a function of the square of the radii
\n" ); document.write( "--> Area of the large circle = area*(1 + sqrt(2))^2
\n" ); document.write( "Area of the quadrant = (area*(1 + sqrt(2))^2)/4
\n" ); document.write( "AQ/a = (1 + 2 + 2sqrt(2))/4 = (3 + 2sqrt(2))/4
\n" ); document.write( "--> ratio of small circle to quadrant = 4/(3 + 2sqrt(2))
\n" ); document.write( "= 4(3 - 2sqrt(2)) to 1
\n" ); document.write( "=~ 0.68629 \n" ); document.write( "