document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040661>Question 1040661</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the circle if a triangle whose sides lie on the lines 3x+4y=8, 3x-4y=32 and x-8=0 inscribed the circle.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655550 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=655550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the intersection points.<BR>\n" );
document.write( "From eq. 3,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8 ALIGN=MIDDLE  ALT=\"x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting into eq. 1,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%288%29%2B4y=8 ALIGN=MIDDLE  ALT=\"3%288%29%2B4y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2B4y=8 ALIGN=MIDDLE  ALT=\"24%2B4y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=-16 ALIGN=MIDDLE  ALT=\"4y=-16\"   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 ALIGN=MIDDLE  ALT=\"y=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(8,-4)<BR>\n" );
document.write( "Substituting into eq. 2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%288%29-4y=32 ALIGN=MIDDLE  ALT=\"3%288%29-4y=32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24-4y=32 ALIGN=MIDDLE  ALT=\"24-4y=32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4y=8 ALIGN=MIDDLE  ALT=\"-4y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2 ALIGN=MIDDLE  ALT=\"y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(8,-2)<BR>\n" );
document.write( "Finally adding eq. 1 and eq. 2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y%2B3x-4y=8%2B32 ALIGN=MIDDLE  ALT=\"3x%2B4y%2B3x-4y=8%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x=40 ALIGN=MIDDLE  ALT=\"6x=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=40%2F6 ALIGN=MIDDLE  ALT=\"x=40%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=20%2F3 ALIGN=MIDDLE  ALT=\"x=20%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2820%2F3%29%2B4y=8 ALIGN=MIDDLE  ALT=\"3%2820%2F3%29%2B4y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2B4y=8 ALIGN=MIDDLE  ALT=\"20%2B4y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=-12 ALIGN=MIDDLE  ALT=\"4y=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3 ALIGN=MIDDLE  ALT=\"y=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(20/3,-3)<BR>\n" );
document.write( "Now you have three points on the circle, solve for the circle.<BR>\n" );
document.write( "Use the general form,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2BDx%2BEy%2BF=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2BDx%2BEy%2BF=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(8,-4):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%5E2%2B%28-4%29%5E2%2B8D-4E%2BF=0 ALIGN=MIDDLE  ALT=\"8%5E2%2B%28-4%29%5E2%2B8D-4E%2BF=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2B16%2B8D-4E%2BF=0 ALIGN=MIDDLE  ALT=\"64%2B16%2B8D-4E%2BF=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8D-4E%2BF=-80 ALIGN=MIDDLE  ALT=\"8D-4E%2BF=-80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(8,-2):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%5E2%2B%28-2%29%5E2%2B8D-2E%2BF=0 ALIGN=MIDDLE  ALT=\"8%5E2%2B%28-2%29%5E2%2B8D-2E%2BF=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2B4%2B8D-2E%2BF=0 ALIGN=MIDDLE  ALT=\"64%2B4%2B8D-2E%2BF=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8D-2E%2BF=-68 ALIGN=MIDDLE  ALT=\"8D-2E%2BF=-68\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(20/3,-3):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820%2F3%29%5E2%2B%28-3%29%5E2%2B%2820%2F3%29D-3E%2BF=0 ALIGN=MIDDLE  ALT=\"%2820%2F3%29%5E2%2B%28-3%29%5E2%2B%2820%2F3%29D-3E%2BF=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400%2F9%2B9%2B%2820%2F3%29D-3E%2BF=0 ALIGN=MIDDLE  ALT=\"400%2F9%2B9%2B%2820%2F3%29D-3E%2BF=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400%2B81%2B60D-27E%2B9F=0 ALIGN=MIDDLE  ALT=\"400%2B81%2B60D-27E%2B9F=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "6.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60D-27E%2B9F=-481 ALIGN=MIDDLE  ALT=\"60D-27E%2B9F=-481\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtracting eq. 5 from eq. 4,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8D-4E%2BF-8D%2B2E-F=-80%2B68 ALIGN=MIDDLE  ALT=\"8D-4E%2BF-8D%2B2E-F=-80%2B68\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2E=-12 ALIGN=MIDDLE  ALT=\"-2E=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E=-6 ALIGN=MIDDLE  ALT=\"E=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting into eq. 4,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8D-4%286%29%2BF=-80 ALIGN=MIDDLE  ALT=\"8D-4%286%29%2BF=-80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "7.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8D%2BF=56 ALIGN=MIDDLE  ALT=\"8D%2BF=56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting into eq. 6,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60D-27%286%29%2B9F=-481 ALIGN=MIDDLE  ALT=\"60D-27%286%29%2B9F=-481\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "8.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60D%2B9F=-319 ALIGN=MIDDLE  ALT=\"60D%2B9F=-319\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply eq. 7 by -9 and add to eq. 8,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-72D-9F%2B60D%2B9F=504-319 ALIGN=MIDDLE  ALT=\"-72D-9F%2B60D%2B9F=504-319\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12D=185 ALIGN=MIDDLE  ALT=\"-12D=185\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=-185%2F12 ALIGN=MIDDLE  ALT=\"D=-185%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and substituting into eq. 7,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%28-185%2F12%29%2BF=-56 ALIGN=MIDDLE  ALT=\"8%28-185%2F12%29%2BF=-56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F=-672%2F12%2B1480%2F12 ALIGN=MIDDLE  ALT=\"F=-672%2F12%2B1480%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F=808%2F12 ALIGN=MIDDLE  ALT=\"F=808%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F=202%2F3 ALIGN=MIDDLE  ALT=\"F=202%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2-%28185%2F12%29x%2B6y%2B202%2F3=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-%28185%2F12%29x%2B6y%2B202%2F3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can complete the square to get into center-radius form,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-%28185%2F12%29x%29%2B%28y%5E2%2B6y%29%2B202%2F3=0 ALIGN=MIDDLE  ALT=\"%28x%5E2-%28185%2F12%29x%29%2B%28y%5E2%2B6y%29%2B202%2F3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-%28185%2F12%29x%2B%28185%2F24%29%5E2%29%2B%28y%5E2%2B6y%2B9%29=%28185%2F24%29%5E2%2B9-202%2F3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-185%2F24%29%5E2%2B%28y%2B3%29%5E2=34225%2F576%2B5184%2F576-38784%2F576 ALIGN=MIDDLE  ALT=\"%28x-185%2F24%29%5E2%2B%28y%2B3%29%5E2=34225%2F576%2B5184%2F576-38784%2F576\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-185%2F24%29%5E2%2B%28y%2B3%29%5E2=625%2F576 ALIGN=MIDDLE  ALT=\"%28x-185%2F24%29%5E2%2B%28y%2B3%29%5E2=625%2F576\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-185%2F24%29%5E2%2B%28y%2B3%29%5E2=%2825%2F24%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-185%2F24%29%5E2%2B%28y%2B3%29%5E2=%2825%2F24%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Center : (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=185%2F24 ALIGN=MIDDLE  ALT=\"185%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Radius : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F24 ALIGN=MIDDLE  ALT=\"25%2F24\"   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=dfc7.JPG\">. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );