document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195525>Question 1195525</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove the following theorem: There exists one circumcircle for any triangle, or any triangle is cyclic. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #828037 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52879)</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=828037\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Usually and traditionally in &nbsp;Geometry, &nbsp;this statement is formulated in this &nbsp;EQUIVALENT &nbsp;form\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Three perpendicular bisectors of a triangle sides are concurrent, &nbsp;in other words, &nbsp;they intersect at one point.\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This intersection point is equidistant from the three triangle vertices and is the center of the circumscribed circle of the triangle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For the proof, &nbsp;see the lesson\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Triangles/Perpendicular-bisectors-of-a-triangle-sides-are-concurrent.lesson>Perpendicular bisectors of a triangle sides are concurrent</A>\r<BR>\n" );
document.write( "\n" );
document.write( "in this site.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "/////////////////////\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "At this site, &nbsp;you have free of charge online textbook on Geometry\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;<A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A> \r<BR>\n" );
document.write( "\n" );
document.write( "in this site.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The referred lesson is the part of this online textbook under the topic &nbsp;\"<U>Properties of triangles</U>\".\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Save the link to this online textbook together with its description\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Free of charge online textbook in GEOMETRY<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to your archive and use it when it is needed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This textbook contains &nbsp;whole/(entire) &nbsp;standard high-school \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Geometry curriculum in its logical development from &nbsp;\" a \" &nbsp;to &nbsp;\" Z \".\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Euclid retold online in English by me and in my own words, \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;as I remember it from my high school years.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );