document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=436544>Question 436544</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi am slightly stuck on this question in geometry\r<BR>\n" );
document.write( "\n" );
document.write( "Given a triangle ABC prove that:\r<BR>\n" );
document.write( "\n" );
document.write( "abc=4&#8710;R where &#8710; is the area of the triangle and R is the radius of the circumcircle of the triangle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #302044 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=302044\">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%2C0%2C10%2C0%2C10%2C%0D%0A%0D%0A%0D%0Atriangle%282%2C2%2C9%2C2%2C5%2C8%29%2C%0D%0Aline%285.5%2C4%2C2%2C2%29%2C%0D%0Aline%285.5%2C4%2C9%2C2%29%2C%0D%0Aline%285.5%2C4%2C5%2C8%29%2C%0D%0Alocate%282%2C2%2CA%29%2C%0D%0Alocate%285%2C8.5%2CB%29%2C%0D%0Alocate%289%2C2%2CC%29%0D%0A%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Assume a,b,c are the side lengths opposite vertices A,B,C respectively. From the extended law of sines,\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fsin%28A%29+=+b%2Fsin%28B%29+=+c%2Fsin%28C%29+=+2R ALIGN=MIDDLE  ALT=\"a%2Fsin%28A%29+=+b%2Fsin%28B%29+=+c%2Fsin%28C%29+=+2R\"   DISABLED_style= \"max-width:90%; height:auto;\" >; this implies <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29+=+a%2F2R ALIGN=MIDDLE  ALT=\"sin%28A%29+=+a%2F2R\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note that the area of the triangle is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA+=+bc%2Asin%28A%29%2F2 ALIGN=MIDDLE  ALT=\"DELTA+=+bc%2Asin%28A%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We can substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29 ALIGN=MIDDLE  ALT=\"sin%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to obtain\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA+=+bc%28a%2F2R%29%2F2 ALIGN=MIDDLE  ALT=\"DELTA+=+bc%28a%2F2R%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA+=+abc%2F4R ALIGN=MIDDLE  ALT=\"DELTA+=+abc%2F4R\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abc+=+4R%2ADELTA ALIGN=MIDDLE  ALT=\"abc+=+4R%2ADELTA\"   DISABLED_style= \"max-width:90%; height:auto;\" > as desired. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );