document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1116523>Question 1116523</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a circle is inscribed in a square and circumscribed about another. detrermine the ratio of the area of the larger square to the area of smaller square. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #731416 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=731416\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The drawing for this situation is:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28300%2C300%2C-5%2C5%2C-5%2C5%2C+grid%280%29%2C%0D%0A+++++++++++++++++++++++line%28-4%2C-4%2C-4%2C4%29%2C%0D%0A+++++++++++++++++++++++line%28-4%2C4%2C4%2C4%29%2C%0D%0A+++++++++++++++++++++++line%284%2C4%2C4%2C-4%29%2C%0D%0A+++++++++++++++++++++++line%284%2C-4%2C-4%2C-4%29%2C%0D%0A++++++++++++++++++++++green%28line%28-2.8%2C-2.8%2C-2.8%2C+2.8%29%29%2C%0D%0A++++++++++++++++++++++green%28line%28-2.8%2C2.8%2C2.8%2C+2.8%29%29%2C%0D%0A++++++++++++++++++++++green%28line%282.8%2C2.8%2C2.8%2C-2.8%29%29%2C%0D%0A++++++++++++++++++++++green%28line%282.8%2C-2.8%2C-2.8%2C+-2.8%29%29%2C++%0D%0A++++++++++++++++++++++circle%280%2C0%2C4%29%0D%0A%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Let d=diameter of the circle.<BR>\n" );
document.write( "The small square has a diagonal length of  d, so the sides are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%2Fsqrt%282%29+ ALIGN=MIDDLE  ALT=\"+d%2Fsqrt%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units long.<BR>\n" );
document.write( "The large square has sides that are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+ ALIGN=MIDDLE  ALT=\"+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units long.\r<BR>\n" );
document.write( "\n" );
document.write( "So the ratio of large to small is   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28d%5E2%29%2F+%28%28d%5E2%2F2%29%29+=+highlight%28+2+%2F+1+%29++ ALIGN=MIDDLE  ALT=\"+%28d%5E2%29%2F+%28%28d%5E2%2F2%29%29+=+highlight%28+2+%2F+1+%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28+2%3A1+%29+ ALIGN=MIDDLE  ALT=\"+highlight%28+2%3A1+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧\r<BR>\n" );
document.write( "\n" );
document.write( "What tutor greenestamps says is correct.  If one draws the inner square as below, the 2:1 ratio in the areas is much more obvious. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28300%2C300%2C-5%2C5%2C-5%2C5%2C+grid%280%29%2C%0D%0A+++++++++++++++++++++++line%28-4%2C-4%2C-4%2C4%29%2C%0D%0A+++++++++++++++++++++++line%28-4%2C4%2C4%2C4%29%2C%0D%0A+++++++++++++++++++++++line%284%2C4%2C4%2C-4%29%2C%0D%0A+++++++++++++++++++++++line%284%2C-4%2C-4%2C-4%29%2C%0D%0A++++++++++++++++++++++green%28line%28-4%2C0%2C0%2C4%29%29%2C%0D%0A++++++++++++++++++++++green%28line%280%2C4%2C4%2C0%29%29%2C%0D%0A++++++++++++++++++++++green%28line%284%2C0%2C0%2C-4%29%29%2C%0D%0A++++++++++++++++++++++green%28line%280%2C-4%2C-4%2C0%29%29%2C++%0D%0A++++++++++++++++++++++circle%280%2C0%2C4%29%0D%0A%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );