document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133723>Question 1133723</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three circles of radius two cm overlap so that each passes through the Center of the other two.        (Basically a triple Venn diagram.) What is the area of the region that would be in the middle, in cm^2? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #750965 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=750965\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB ALIGN=MIDDLE  ALT=\"AB\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC ALIGN=MIDDLE  ALT=\"AC\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC ALIGN=MIDDLE  ALT=\"BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > are all radii, so they are all equal, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC ALIGN=MIDDLE  ALT=\"ABC\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an equilateral triangles and all the angles are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees.\r<BR>\n" );
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document.write( " area of triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC=%281%2F2%29ab%2Asin%2860%29 ALIGN=MIDDLE  ALT=\"ABC=%281%2F2%29ab%2Asin%2860%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=r ALIGN=MIDDLE  ALT=\"a=r\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b=r ALIGN=MIDDLE  ALT=\"+b=r\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC=%281%2F2%29r%5E2%2A%28sqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"ABC=%281%2F2%29r%5E2%2A%28sqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC=%28r%5E2%2Asqrt%283%29%29%2F4 ALIGN=MIDDLE  ALT=\"ABC=%28r%5E2%2Asqrt%283%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now I want to know what the area of minor segment<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+AB ALIGN=MIDDLE  ALT=\"+AB\"   DISABLED_style= \"max-width:90%; height:auto;\" > is on the circle centered at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "segment area=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2860%2F360%29%2Ar%5E2%2Api+-%28r%5E2%2Asqrt%283%29%29%2F4 ALIGN=MIDDLE  ALT=\"+%2860%2F360%29%2Ar%5E2%2Api+-%28r%5E2%2Asqrt%283%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "segment area= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F12%29%2Ar%5E2%2Api+-%283r%5E2%2Asqrt%283%29%29%2F12 ALIGN=MIDDLE  ALT=\"%282%2F12%29%2Ar%5E2%2Api+-%283r%5E2%2Asqrt%283%29%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "segment area= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Ar%5E2%2Api+-3r%5E2%2Asqrt%283%29%29%2F12 ALIGN=MIDDLE  ALT=\"%282%2Ar%5E2%2Api+-3r%5E2%2Asqrt%283%29%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> now\r<BR>\n" );
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document.write( "shadedarea=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%282%2Ar%5E2%2Api+-3r%5E2%2Asqrt%283%29%29%2F12+%2B%28r%5E2%2Asqrt%283%29%29%2F4 ALIGN=MIDDLE  ALT=\"3%2A%282%2Ar%5E2%2Api+-3r%5E2%2Asqrt%283%29%29%2F12+%2B%28r%5E2%2Asqrt%283%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "shadedarea=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%283%29%2A%282%2Ar%5E2%2Api+-3r%5E2%2Asqrt%283%29%29%2Fcross%2812%294+%2B%28r%5E2%2Asqrt%283%29%29%2F4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "shadedarea=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Ar%5E2%2Api+-3r%5E2%2Asqrt%283%29%29%2F4+%2B%28r%5E2%2Asqrt%283%29%29%2F4 ALIGN=MIDDLE  ALT=\"%282%2Ar%5E2%2Api+-3r%5E2%2Asqrt%283%29%29%2F4+%2B%28r%5E2%2Asqrt%283%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "shadedarea=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Ar%5E2%2Api+-3r%5E2%2Asqrt%283%29+%2Br%5E2%2Asqrt%283%29%29%2F4 ALIGN=MIDDLE  ALT=\"%282%2Ar%5E2%2Api+-3r%5E2%2Asqrt%283%29+%2Br%5E2%2Asqrt%283%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "shadedarea=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Ar%5E2%2Api+-2r%5E2%2Asqrt%283%29%29%2F4 ALIGN=MIDDLE  ALT=\"%282%2Ar%5E2%2Api+-2r%5E2%2Asqrt%283%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "shadedarea=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%282%29%2Ar%5E2%2Api+-cross%282%29r%5E2%2Asqrt%283%29%29%2Fcross%284%292 ALIGN=MIDDLE  ALT=\"%28cross%282%29%2Ar%5E2%2Api+-cross%282%29r%5E2%2Asqrt%283%29%29%2Fcross%284%292\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "shadedarea=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%5E2%2Api+-r%5E2%2Asqrt%283%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28r%5E2%2Api+-r%5E2%2Asqrt%283%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "shadedarea=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%5E2%2F2%29%28pi+-sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%28r%5E2%2F2%29%28pi+-sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=2cm ALIGN=MIDDLE  ALT=\"r=2cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the area of the shaded region is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=shadedarea=%28%282cm%29%5E2%2F2%29%28pi-sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"shadedarea=%28%282cm%29%5E2%2F2%29%28pi-sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=shadedarea=%284cm%5E2%2F2%29%28pi-sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"shadedarea=%284cm%5E2%2F2%29%28pi-sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=shadedarea=+2cm%5E2%28pi-sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"shadedarea=+2cm%5E2%28pi-sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=shadedarea=2.8190cm%5E2 ALIGN=MIDDLE  ALT=\"shadedarea=2.8190cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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