document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198960>Question 1198960</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The vertices of a square are the centers of four circles as shown below. The two big circles touch each other and also the two little circles. With which factor do you have to multiply the radius of the little circles to obtain the radius of the big circle?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832648 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832648\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Here is a diagram:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C0%2C800%2C0%2C800%0D%0A%2Cline%28200%2C200%2C500%2C200%29%2Cline%28200%2C200%2C200%2C500%29%2Cline%28500%2C200%2C500%2C500%29%2Cline%28200%2C500%2C500%2C500%29%0D%0A%2Ccircle%28200%2C200%2C150%2Asqrt%282%29%29%2Ccircle%28500%2C500%2C150%2Asqrt%282%29%29%0D%0A%2Ccircle%28500%2C200%2C300-150%2Asqrt%282%29%29%2Ccircle%28200%2C500%2C300-150%2Asqrt%282%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the side length of the square.  Then...<BR>\n" );
document.write( "the diagonal of the square is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"2x%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so the radius of the larger circles is <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;\" >,<BR>\n" );
document.write( "so the radius of the smaller circles is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-x%2Asqrt%282%29=x%282-sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"2x-x%2Asqrt%282%29=x%282-sqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The problem asks for the factor by which the radius of the smaller circles has to be multiplied to get the radius of the larger circles.  That factor is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2A%28sqrt%282%29%29%29%2F%28x%2A%282-sqrt%282%29%29%29=%28sqrt%282%29%29%2F%282-sqrt%282%29%29=%28%28sqrt%282%29%29%282%2Bsqrt%282%29%29%29%2F%28%282-sqrt%282%29%29%282%2Bsqrt%282%29%29%29=%282%2Asqrt%282%29%2B2%29%2F%284-2%29=%282%2Asqrt%282%29%2B2%29%2F2=sqrt%282%29%2B1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2B1 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );