document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=347856>Question 347856</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circle is inscribed in a square, which is circumscribed by another circle. If the diagonal of  square is 2x, find the ratio of the area of the large circle to the area of the small circle?    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #248755 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=248755\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A circle is inscribed in a square, which is circumscribed by another circle.<BR>\n" );
document.write( " If the diagonal of square is 2x, find the ratio of the area of the large<BR>\n" );
document.write( " circle to the area of the small circle?<BR>\n" );
document.write( ";<BR>\n" );
document.write( "x = the radius of the large circle<BR>\n" );
document.write( "then<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ax%5E2 ALIGN=MIDDLE  ALT=\"pi%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >; the area of the larger circle<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the area of the small circle<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = side of the square, given that 2x = diagonal of the square<BR>\n" );
document.write( "s^2 + s^2 = (2x)^2<BR>\n" );
document.write( "2s^2 = 4x^2<BR>\n" );
document.write( "Divide both sides by 2<BR>\n" );
document.write( "s^2 = 2x^2<BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282x%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%282x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"x%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the side of the square<BR>\n" );
document.write( ":<BR>\n" );
document.write( "the side of the square is also the diameter of the small circle,therefore:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Asqrt%282%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28x%2Asqrt%282%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the radius of the small circle<BR>\n" );
document.write( "Find the area of the small circle<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A%28x%2Asqrt%282%29%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"pi%2A%28x%2Asqrt%282%29%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Which is:<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A%28%282x%5E2%29%2F4%29 ALIGN=MIDDLE  ALT=\"pi%2A%28%282x%5E2%29%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel 2<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A%28x%5E2%2F2%29 ALIGN=MIDDLE  ALT=\"pi%2A%28x%5E2%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "large area<BR>\n" );
document.write( "---------- would be:<BR>\n" );
document.write( "small area\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%2Ax%5E2%29%2F%28pi%2A%28x%5E2%2F2%29%29 ALIGN=MIDDLE  ALT=\"%28pi%2Ax%5E2%29%2F%28pi%2A%28x%5E2%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%281%2F2%29 ALIGN=MIDDLE  ALT=\"1%2F%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F1 ALIGN=MIDDLE  ALT=\"2%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >; canceled pi*x^2<BR>\n" );
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