document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1065525>Question 1065525</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the circumcenter of a triangle with a vertices of (2,4), (6,4), (2, 6)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #680685 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=680685\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the midpoints of the sides,<BR>\n" );
document.write( "A(2,4)<BR>\n" );
document.write( "B(2,6)<BR>\n" );
document.write( "C(6,4)<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "To find the midpoint, take the averages of the x and y values,<BR>\n" );
document.write( "Midpoint of AC: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B6%29%2F2 ALIGN=MIDDLE  ALT=\"%282%2B6%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2B4%29%2F2 ALIGN=MIDDLE  ALT=\"%284%2B4%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(4,4)<BR>\n" );
document.write( "Midpoint of AB: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B2%29%2F2 ALIGN=MIDDLE  ALT=\"%282%2B2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2B6%29%2F2 ALIGN=MIDDLE  ALT=\"%284%2B6%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(2,5)<BR>\n" );
document.write( "Midpoint of BC: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B6%29%2F2 ALIGN=MIDDLE  ALT=\"%282%2B6%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2B4%29%2F2 ALIGN=MIDDLE  ALT=\"%286%2B4%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(4,5)<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "Now find the lines through mAC and B(line 1), mAB and C(line 2), and mBC and A(line 3).<BR>\n" );
document.write( "First find the slope, then use the point slope form of a line,<BR>\n" );
document.write( "I'll use the designation 1, 2, 3 for the lines as defined in the previous sentence.<BR>\n" );
document.write( "Line 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D=%284-6%29%2F%284-2%29=-2%2F2=-1 ALIGN=MIDDLE  ALT=\"m%5B1%5D=%284-6%29%2F%284-2%29=-2%2F2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-4=-1%28x-4%29 ALIGN=MIDDLE  ALT=\"y-4=-1%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-4=-x%2B4 ALIGN=MIDDLE  ALT=\"y-4=-x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=-x%2B8 ALIGN=MIDDLE  ALT=\"y%5B1%5D=-x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Line 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D=%285-4%29%2F%282-6%29=1%2F%28-4%29=-1%2F4 ALIGN=MIDDLE  ALT=\"m%5B2%5D=%285-4%29%2F%282-6%29=1%2F%28-4%29=-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5=-%281%2F4%29%28x-2%29 ALIGN=MIDDLE  ALT=\"y-5=-%281%2F4%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5=-x%2F4%2B1%2F2 ALIGN=MIDDLE  ALT=\"y-5=-x%2F4%2B1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2F4%2B1%2F2%2B10%2F2 ALIGN=MIDDLE  ALT=\"y=-x%2F4%2B1%2F2%2B10%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D=-x%2F4%2B11%2F2 ALIGN=MIDDLE  ALT=\"y%5B2%5D=-x%2F4%2B11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now that we have two lines, we can calculate their intersection (which is the circumcenter),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B8=-x%2F4%2B11%2F2 ALIGN=MIDDLE  ALT=\"-x%2B8=-x%2F4%2B11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%2B32=-x%2B22 ALIGN=MIDDLE  ALT=\"-4x%2B32=-x%2B22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x=-10 ALIGN=MIDDLE  ALT=\"-3x=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BCC%5D=10%2F3 ALIGN=MIDDLE  ALT=\"x%5BCC%5D=10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-10%2F3%2B8 ALIGN=MIDDLE  ALT=\"y=-10%2F3%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-10%2F3%2B24%2F3 ALIGN=MIDDLE  ALT=\"y=-10%2F3%2B24%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5BCC%5D=14%2F3 ALIGN=MIDDLE  ALT=\"y%5BCC%5D=14%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=af7.JPG\">. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );