document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=806516>Question 806516</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ABC is a triangel. N is a point inside the triangel. Prove that:\r<BR>\n" );
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document.write( "AN+BN+CN > 1/2 (AB+BC+AC) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #485894 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=485894\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In any triangle, sum of any two sides is always greater than the third.\r<BR>\n" );
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document.write( "Consider the triangle ABN:<BR>\n" );
document.write( "AN + BN > AB _______________ (1)\r<BR>\n" );
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document.write( "Consider the triangle BCN:<BR>\n" );
document.write( "BN + CN > BC _______________ (2)\r<BR>\n" );
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document.write( "Consider the triangle ACN:<BR>\n" );
document.write( "AN + CN > AC _______________ (3)\r<BR>\n" );
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document.write( "Adding both sides of (1), (2) and (3) we have\r<BR>\n" );
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document.write( "AN + BN + BN + CN + CN + AN > AB + BC + AC<BR>\n" );
document.write( "2(AN + BN + CN) > AB + BC + AC<BR>\n" );
document.write( "AN + BN + CN > (AB + BC + AC)/2\r<BR>\n" );
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document.write( "Hence proved </SPAN>\n" );
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