document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=891679>Question 891679</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three identical circles are tangent to each other externally. If the area of the curvilinear triangle enclosed between the points of tangency of the 3 circles is 16.13, compute the radius of each circle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #539940 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=539940\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-8%2C8%2C-6%2C10%2Cgrid%281%29%2Ccircle%28-5%2C0%2C5%29%2Ccircle%285%2C0%2C5%29%2Ccircle%280%2C8.66%2C5%29%2Cblue%28line%28-5%2C0%2C0%2C8.66%29%29%2Cgreen%28arc%280%2C8.66%2C10%2C10%2C60%2C120%29%29%2Cgreen%28arc%285%2C0%2C10%2C10%2C-180%2C-120%29%29%2Cgreen%28arc%28-5%2C0%2C10%2C10%2C-60%2C0%29%29%2Cblue%28line%280%2C8.66%2C5%2C0%29%29%2Cblue%28line%285%2C0%2C-5%2C0%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The diagram helps to solve the problem. <BR>\n" );
document.write( "Calculate the area of the large blue triangle.<BR>\n" );
document.write( "Calculate the circular sector areas.<BR>\n" );
document.write( "Subtract to get the area of the curvilinear triangle.<BR>\n" );
document.write( "Blue triangle - Equilateral triangle with side 2R.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BET%5D=%28sqrt%283%29%2F4%29s%5E2 ALIGN=MIDDLE  ALT=\"A%5BET%5D=%28sqrt%283%29%2F4%29s%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BET%5D=%28sqrt%283%29%2F4%29%282R%29%5E2 ALIGN=MIDDLE  ALT=\"A%5BET%5D=%28sqrt%283%29%2F4%29%282R%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BET%5D=sqrt%283%29R%5E2 ALIGN=MIDDLE  ALT=\"A%5BET%5D=sqrt%283%29R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Circular sector : Each sector is 60 degrees. The whole circle is 360 degrees.<BR>\n" );
document.write( "So the area of each circular sector is 1/6 of the whole circle area.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BCS%5D=%28pi%2F6%29R%5E2 ALIGN=MIDDLE  ALT=\"A%5BCS%5D=%28pi%2F6%29R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since there are 3 circular sector within the equilateral triangle,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BCST%5D=%28pi%2F2%29R%5E2 ALIGN=MIDDLE  ALT=\"A%5BCST%5D=%28pi%2F2%29R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then the area of the curvilinear triangle is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BCT%5D=A%5BET%5D-A%5BCST%5D ALIGN=MIDDLE  ALT=\"A%5BCT%5D=A%5BET%5D-A%5BCST%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BCT%5D=sqrt%283%29R%5E2-%28pi%2F2%29R%5E2=16.13 ALIGN=MIDDLE  ALT=\"A%5BCT%5D=sqrt%283%29R%5E2-%28pi%2F2%29R%5E2=16.13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29-pi%2F2%29R%5E2=16.13 ALIGN=MIDDLE  ALT=\"%28sqrt%283%29-pi%2F2%29R%5E2=16.13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2=16.13%2F%281.73-1.57%29 ALIGN=MIDDLE  ALT=\"R%5E2=16.13%2F%281.73-1.57%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2=16.13%2F0.1613 ALIGN=MIDDLE  ALT=\"R%5E2=16.13%2F0.1613\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2=100.03 ALIGN=MIDDLE  ALT=\"R%5E2=100.03\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=10 ALIGN=MIDDLE  ALT=\"R=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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