document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936245>Question 936245</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many circles are determined by nine points? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569846 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=569846\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your question is too vague. For any three points in the plane, not all collinear, there is a unique circle that passes through those points, in which the number of circles is at most 9C3 = 84, assuming no two circles are the same. Or you could be referring to the famous nine-point circle of a triangle, which is determined by the midpoints of the sides, the feet of the altitudes, and the midpoints of the lines from the sides to the orthocenter. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );