document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88427>Question 88427</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation of a circle with centre O(0, 0) is x² + y² = 10.  The points C(3, 1) and D(1, -3) are the endpoints of chord CD.  EF right bisects chord CD at G.  Verify that the centre of the circle lies on the right bisector of chord CD.\r<BR>\n" );
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document.write( "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 #64269 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=64269\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation of a circle with centre O(0, 0) is x² + y² = 10.  The points C(3, 1) and D(1, -3) are the endpoints of chord CD.  EF right bisects chord CD at G.  Verify that the centre of the circle lies on the right bisector of chord CD<BR>\n" );
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document.write( "The coordinates of G are those of the midpoint of CD = [(3+1)/2,(1+-3)/2]=(2,-1)<BR>\n" );
document.write( "The slope of CD = (1--3)/(3-1)=2<BR>\n" );
document.write( "Therefore the slope of the perpendicular bisector is -1/2<BR>\n" );
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document.write( "Find the equation of the line with slope -1/2 thru point (2,-1)<BR>\n" );
document.write( "-1=(-1/2)(2)+b<BR>\n" );
document.write( "b = 0<BR>\n" );
document.write( "EQUATION is y=(-1/2)x<BR>\n" );
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document.write( "The center of the circle is given as (0,0)<BR>\n" );
document.write( "It is on the line y=(-1/2)x because 0=(-1/2)*0<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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