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geometry > Euclidean geometry > Ceva's theorem

geometry > affine geometry > Ceva's theorem

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Ceva's theorem

In Euclidean geometry, Ceva's theorem is a theorem about triangles. Given a triangle $△ ABC$ , let the lines $AO, BO, CO$ be drawn from the vertices to a common point $O$ (not on one of the sides of $△ ABC$ ), to meet opposite sides at $D, E, F$ respectively. (The segments $AD, BE, CF$ are known as cevians.) Then, using signed lengths of segments,

${\\displaystyle {\ rac {\\overline {AF}}{\\overline {FB}}}\\cdot {\ rac {\\overline {BD}}{\\overline {DC}}}\\cdot {\ rac {\\overline {CE}}{\\overline {EA}}}=1.}$

In other words, the length $XY$ is taken to be positive or negative according to whether $X$ is to the left or right of $Y$ in some fixed orientation of the line. For example, $AF / FB$ is defined as having positive value when $F$ is between $A$ and $B$ and negative otherwise.

(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Ceva%27s_theorem)

théorème de Ceva

francés

URI

http://data.loterre.fr/ark:/67375/PSR-WS61VZXF-C

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