Menelaus' Theorem
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Menelaus' Theorem deals with the collinearity of points on each of the three sides (extended when necessary) of a triangle. It is named for Menelaus of Alexandria.
Statement
A necessary and sufficient condition for points on the respective side lines
of a triangle
to be collinear is that
![$BD\cdot CE\cdot AF = -DC\cdot EA\cdot FB$](http://latex.artofproblemsolving.com/0/4/5/045a215225c903c05bd169d618043067ce17cd8d.png)
where all segments in the formula are directed segments.