document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026227>Question 1026227</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three circles of radius 1 unit fit inside a square such that the two outer circles touch the middle<BR>\n" );
document.write( "circle and the sides of the square, as shown. Given the centres of the circle lie on the diagonal<BR>\n" );
document.write( "of the square, find the exact area of the square.\r<BR>\n" );
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document.write( "http://imgur.com/2wZdTkq\r<BR>\n" );
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document.write( "Please incldue all working out. Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641463 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=641463\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look at either circle near one of the corners of the square.  Draw a radius which intersects a side of the square; which is also tangent to the circle.  This tangency point, and the center point of the circle, and the corner of the square, form a right isosceles triangle having two sides of 1 unit.  The hypotenuse can be found:\r<BR>\n" );
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document.write( "h for this hypotenuse, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=sqrt%281%5E2%2B1%5E2%29=sqrt%282%29 ALIGN=MIDDLE  ALT=\"h=sqrt%281%5E2%2B1%5E2%29=sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You can find the length of the diagonal of the square.  The diagonal contains SIX of the radii lengths (of any of the circles); but also understand the distance from corner to a nearest center of a circle...<BR>\n" );
document.write( "and revise the sum of lengths which compose the diagonal of the outer square.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2Br%2B2r%2Br%2Bsqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2Br%2B2r%2Br%2Bsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----the length of the diagonal of the square, which simplified is...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%284r%2B2sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%284r%2B2sqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "If this solution is stopped here, can you finish answering the question? </SPAN>\n" );
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