document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=319456>Question 319456</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the co ordinate of the centre of a circle which passes through the points A(1,2),B(3,-4) and C(5,-6).Also find the radius of 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 #228880 by </B><A HREF=/tutors/aboutme.mpl?userid=Greenfinch><B>Greenfinch(383)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Greenfinch><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=Greenfinch><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=228880\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Chord AB has gradient -6/2 or -3. Chord AC has gradient -8/4 or -2<BR>\n" );
document.write( "Perpendicular lines therefore have gradients of 1/2 and 1/3 respectively.<BR>\n" );
document.write( "The perpendicular will go through the mid point of the chord or (2,-1) and (3,-2)<BR>\n" );
document.write( "The line going through(2,-1) with a gradient of 1/3 is y=1/3x -5/3<BR>\n" );
document.write( "The line going through (3,-2) with a gradient of 1/2 is y = 1/2x - 7/2<BR>\n" );
document.write( "re-arrange to 3y - x = 5 and 2y - x = 7<BR>\n" );
document.write( "Solve simultaneously to get y = 2, which gives x = 11<BR>\n" );
document.write( "So centre of circle is (11,2).<BR>\n" );
document.write( "Point A is on the circumference, so the radius is (1,2) to (11,2) or 10.<BR>\n" );
document.write( "The equation or the circle is thus (y - 2)^2 + (x - 11)^2 = 100 </SPAN>\n" );
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