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Menelaus’ Theorem


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The following theorem, due to Menelaus of Alexandria:

Theorem

Let L, M and N be points on the sides BC, CA and AB of a triangle (possibly extended). Then L, M and N are collinear if and only if

(Note that BC, for example, is considered to be directed from B to C so that LC, for example, is positive if LC is in the same direction as BC and negative if it is in the opposite direction; see measure.) See Ceva's Theorem.

Subjects: Mathematics.


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