document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1043961>Question 1043961</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three circles of radii 8.5, 11.9, and 15.7 cm are mutually tangent. <BR>\n" );
document.write( "Find the area bounded by the three circles.\r<BR>\n" );
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document.write( "area = </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #659207 by </B><A HREF=/tutors/aboutme.mpl?userid=advanced_Learner><B>advanced_Learner(501)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=advanced_Learner><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=advanced_Learner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=659207\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is indeed a classic challenging problem the decimals make it lenghy and hairy ,cant be solved with out drawing,i dont know how to draw three tangent circles but i uploaded an image for you to refer to.\r<BR>\n" );
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document.write( "please refer to picture called \"circles\"\r<BR>\n" );
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document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=advanced_Learner&illustration_name=circles\">.\r<BR>\n" );
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document.write( "first lets find semi-perimeter S of the triangle<BR>\n" );
document.write( "semi-perimeter S of the triangle =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2827.6%2B24.2%2B20.4%29%2F%282%29 ALIGN=MIDDLE  ALT=\"%2827.6%2B24.2%2B20.4%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "              =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36.1 ALIGN=MIDDLE  ALT=\"36.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "area of the triangle=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "area of the triangle=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836.1%2836.1-27.6%29%2836.1-24.2%29%2836.1-20.4%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2836.1%2836.1-27.6%29%2836.1-24.2%29%2836.1-20.4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "area of the triangle=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=239.4343 ALIGN=MIDDLE  ALT=\"239.4343\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "find angle A ,B and C\r<BR>\n" );
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document.write( "NOTE it is not right triangle,use cosine law\r<BR>\n" );
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document.write( "Cos A=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%5E2%2Bc%5E2-a%5E2%29%2F%282bc%29 ALIGN=MIDDLE  ALT=\"%28b%5E2%2Bc%5E2-a%5E2%29%2F%282bc%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >                     <BR>\n" );
document.write( "Cos A=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2827.6%29%5E2%2B%2820.4%29%5E2-%2824.2%29%5E2%29%2F%282%2A27.6%2A20.4%29 ALIGN=MIDDLE  ALT=\"%28%2827.6%29%5E2%2B%2820.4%29%5E2-%2824.2%29%5E2%29%2F%282%2A27.6%2A20.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Cos A=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.520069%29 ALIGN=MIDDLE  ALT=\"%280.520069%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "A=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=58.66 ALIGN=MIDDLE  ALT=\"58.66\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Cos B=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E2%2Bc%5E2-b%5E2%29%2F%282ac%29 ALIGN=MIDDLE  ALT=\"%28a%5E2%2Bc%5E2-b%5E2%29%2F%282ac%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >                     <BR>\n" );
document.write( "Cos B=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2827.6%5E2%29%2B%2824.2%5E2%29-%2820.4%5E2%29%29%2F%282%2A27.6%2A24.2%29 ALIGN=MIDDLE  ALT=\"%28%2827.6%5E2%29%2B%2824.2%5E2%29-%2820.4%5E2%29%29%2F%282%2A27.6%2A24.2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >                     <BR>\n" );
document.write( "Cos B=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.697 ALIGN=MIDDLE  ALT=\"0.697\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "B=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45.81 ALIGN=MIDDLE  ALT=\"45.81\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "cos C=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28180%29-%2858.66%2B45.81%29 ALIGN=MIDDLE  ALT=\"%28180%29-%2858.66%2B45.81%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cos C=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75.53 ALIGN=MIDDLE  ALT=\"75.53\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or use the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=formula ALIGN=MIDDLE  ALT=\"formula\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Cos C=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E2%2Bb%5E2-c%5E2%29%2F%282ab%29 ALIGN=MIDDLE  ALT=\"%28a%5E2%2Bb%5E2-c%5E2%29%2F%282ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cos C=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2824.2%5E2%29%2B%2820.4%5E2%29-%2827.6%5E2%29%29%2F%282%2A24.2%2A20.4%29 ALIGN=MIDDLE  ALT=\"%28%2824.2%5E2%29%2B%2820.4%5E2%29-%2827.6%5E2%29%29%2F%282%2A24.2%2A20.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >                     <BR>\n" );
document.write( "Cos C=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2529 ALIGN=MIDDLE  ALT=\"0.2529\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "C=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75.34 ALIGN=MIDDLE  ALT=\"75.34\"   DISABLED_style= \"max-width:90%; height:auto;\" > very very minor difference\r<BR>\n" );
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document.write( "area sector a=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%2Ar%5E2%2Aangle+A%29%2F%28360%29 ALIGN=MIDDLE  ALT=\"%28pi%2Ar%5E2%2Aangle+A%29%2F%28360%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >                     <BR>\n" );
document.write( "area sector a=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%2A%2811.9%29%5E2%2A%2858.66%29%29%2F%28360%29 ALIGN=MIDDLE  ALT=\"%28pi%2A%2811.9%29%5E2%2A%2858.66%29%29%2F%28360%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >                     <BR>\n" );
document.write( "area sector a=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2872.45%29 ALIGN=MIDDLE  ALT=\"%2872.45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >                     \r<BR>\n" );
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document.write( "area sector b=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%2A%2815.7%29%5E2%2A%2845.8%29%29%2F%28360%29 ALIGN=MIDDLE  ALT=\"%28pi%2A%2815.7%29%5E2%2A%2845.8%29%29%2F%28360%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >                     <BR>\n" );
document.write( "area sector b=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2898.467%29 ALIGN=MIDDLE  ALT=\"%2898.467%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >                     \r<BR>\n" );
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document.write( "area sector c=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%2A%288.5%29%5E2%2A%2875.34%29%29%2F%28360%29 ALIGN=MIDDLE  ALT=\"%28pi%2A%288.5%29%5E2%2A%2875.34%29%29%2F%28360%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "area sector c=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2847.477%29 ALIGN=MIDDLE  ALT=\"%2847.477%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >                     <BR>\n" );
document.write( "                     \r<BR>\n" );
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document.write( "the area bounded by the three circles=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28Area+of+the+triangle%29+-%28sum+of+++sector+A+B+and+C%29%29%29 ALIGN=MIDDLE  ALT=\"%28%28Area+of+the+triangle%29+-%28sum+of+++sector+A+B+and+C%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the area bounded by the three circles=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28239.43%29+-%2872.45%2B98.467%2B47.477%29 ALIGN=MIDDLE  ALT=\"%28239.43%29+-%2872.45%2B98.467%2B47.477%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the area bounded by the three circles=~<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2821cm%5E2%29 ALIGN=MIDDLE  ALT=\"%2821cm%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the answer\r<BR>\n" );
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document.write( "your feedback is welcome\r<BR>\n" );
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document.write( "                    <BR>\n" );
document.write( " </SPAN>\n" );
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