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 $D, E, F$ on the respective side lines $BC, CA, AB$ of a triangle $ABC$ to be collinear is that

$BD\cdot CE\cdot AF = -DC\cdot EA\cdot FB$

where all segments in the formula are directed segments.

Menelaus1.PNG

See also