document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062307>Question 1062307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How can I draw a triangle when the lengths of three angle bisectors are given? Will the length of angles bisectors determine 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 #677204 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52847)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=677204\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "How can I draw a triangle when the lengths of three angle bisectors are given? Will the length of angles bisectors determine the triangle?<BR>\n" );
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document.write( "The answer to your first question is:\r<BR>\n" );
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document.write( "     It is NOT POSSIBLE to construct a triangle using a compass and straightedge if the givens are the lengths of its three angle bisectors.\r\n" );
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document.write( "    In other words, such an algorithm DOES NOT exist for the general case.\r\n" );
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document.write( "It was proved in Russian sources by very authoritative mathematician, and the links in the Internet are on Russian articles. See, for example, \r<BR>\n" );
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document.write( "http://www.mccme.ru/ask/qa/bissect.html \r<BR>\n" );
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document.write( "I don't know the references in English (although they should be, I believe).\r<BR>\n" );
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document.write( "Regarding your second question, see this reference\r<BR>\n" );
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document.write( "Mironescu, Petru; Panaitopol, Laurentiu \"The existence of a triangle with prescribed angle bisector lengths.\" <BR>\n" );
document.write( "American Math. Monthly, 101, No.1, 58-60 (1994).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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