document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203333>Question 203333</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Points X, Y and Z lie on the sides of triangle ABC so that segments AX, BY and CZ, if drawn, would intersect at one interior point P. Using 3 of these 7 points at a time as vertices, how many triangles can be formed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153403 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=153403\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ): Points X, Y and Z lie on the sides of triangle ABC so that segments AX, BY and CZ, if drawn, would intersect at one interior point P. Using 3 of these 7 points at a time as vertices, how many triangles can be formed?<BR>\n" );
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document.write( "Draw the picture.<BR>\n" );
document.write( "Three points determine a triangle unless the three are collinear.<BR>\n" );
document.write( "There are 7C3= 25 sets of three points.<BR>\n" );
document.write( "6 of those sets are collinear.<BR>\n" );
document.write( "Therefore 29 triangles can be formed.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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