document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130118>Question 130118</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi! i have a question on my math homework i have to find the circumcenter of a triangle whose points are L(83,15) S(196,123) and B(22,123). i have found the midpoints which are on line: LS is (139.5,69), SB is (109,123), and LB is 52.5,69). then i found the slope of each line which is: LS 108/113, SB 0, and LB -108/61. then i have tried to find the perpendicular bisector of each but every time i do the same problem i have came out with a different number that equals b. i have tried for a few hours on this problem and i would aprieciate if you could help me find what X (of the circumcenter) would be. Thank you   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #95052 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=95052\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The circumcenter is the center  of a triangle's circumcircle. It can be found as the intersection of the perpendicular bisectors.<BR>\n" );
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document.write( "i have to find the circumcenter of a triangle whose points are <BR>\n" );
document.write( "L(83,15), S(196,123) and B(22,123).<BR>\n" );
document.write( "i have found the midpoints which are on line: <BR>\n" );
document.write( "LS is (139.5,69), SB is (109,123), and LB is (52.5,69). <BR>\n" );
document.write( "then i found the slope of each line which is: <BR>\n" );
document.write( "LS 108/113, SB 0, and LB -108/61<BR>\n" );
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document.write( "Equations:<BR>\n" );
document.write( "Perpendicular bisector of LS:<BR>\n" );
document.write( "Finding the y-intercept.<BR>\n" );
document.write( "69 = (-113/108)139.5 + b<BR>\n" );
document.write( "b = 214.9583333<BR>\n" );
document.write( "Equation of the perp/bisector of LS: y = (-113/108)x-214.959333<BR>\n" );
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document.write( "Perpendicular bisector of SB<BR>\n" );
document.write( "Since SB has slope = 0, the perpendicular is a vertical line thru the<BR>\n" );
document.write( "midpoint (109,123)<BR>\n" );
document.write( "Equation of the perp/bisector of SB is x=109<BR>\n" );
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document.write( "Find the intersection of the two perp/bisectors:<BR>\n" );
document.write( "Substitute x=109 into the perp/bisector of LS:<BR>\n" );
document.write( "y = (-113/108)(109)-214.959333<BR>\n" );
document.write( "y = -329.0056295<BR>\n" );
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document.write( "The circumcenter is (109,-329.0056295)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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