Menelaus's theorem | plane geometry | intermediate level

Episode 83.

Menelaus's theorem | plane geometry | intermediate level.

Branch of mathematics: plane geometry.
Difficulty level: intermediate.

Theorem. Let $ABC$ be a triangle. Let $D$, $E$, $F$ be points on the lines $BC$, $CA$, $AB$ respectively. Then the points $D$, $E$, $F$ are collinear if and only if $\frac{\overrightarrow{BD}}{\overrightarrow{DC}} \cdot \frac{\overrightarrow{CE}}{\overrightarrow{EA}} \cdot \frac{\overrightarrow{AF}}{\overrightarrow{FB}} = -1$.

Mathematics. Geometry. Plane geometry.
#Mathematics #Geometry #PlaneGeometry

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