Loterre: Mathematics: Menelaus's theorem

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Menelaus's theorem

Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle △ABC, and a transversal line that crosses BC, AC, and AB at points D, E, and F respectively, with D, E, and F distinct from A, B, and C. A weak version of the theorem states that

${\\displaystyle {\ rac {|AF|}{|FB|}}\ imes {\ rac {|BD|}{|DC|}}\ imes {\ rac {|CE|}{|EA|}}=1,}$

where "| |" denotes absolute value (i.e., all segment lengths are positive).
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Menelaus%27s_theorem)

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