Van Aubel's theorem about cevians | plane geometry | intermediate level

Episode 89.

Van Aubel's theorem about cevians | plane geometry | intermediate level.

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

Van Aubel's theorem about cevians. Let $ABC$ be a triangle. Let $AA'$, $BB'$, $CC'$ be cevians for point $P$ (that is, let $A'$, $B'$, $C'$ be points on the lines $BC$, $CA$, $AB$ respectively such that the lines $AA'$, $BB'$, $CC'$ intersect at a single point $P$). Then $\frac{\overrightarrow{BP}}{\overrightarrow{PB'}} = \frac{\overrightarrow{BA'}}{\overrightarrow{A'C}} + \frac{\overrightarrow{BC'}}{\overrightarrow{C'A}}$.

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

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