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geometry > geometric drawing > triangle center > Jacobi's theorem

... > geometric figure > point > center > triangle center > Jacobi's theorem

... > Euclidean geometry > point > center > triangle center > Jacobi's theorem

Terme préférentiel

Jacobi's theorem

Définition(s)

In plane geometry, a Jacobi point is a point in the Euclidean plane determined by a triangle $△ ABC$ and a triple of angles $α, β, γ$ . This information is sufficient to determine three points $X, Y, Z$ such that ${\\displaystyle {\egin{aligned}\\angle ZAB&=\\angle YAC&=\\alpha ,\\\\\\angle XBC&=\\angle ZBA&=\eta ,\\\\\\angle YCA&=\\angle XCB&=\\gamma .\\end{aligned}}}$ Then, by a theorem of Karl Friedrich Andreas Jacobi, the lines $AX, BY, CZ$ are concurrent, at a point $N$ called the Jacobi point.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Jacobi%27s_theorem_(geometry))

Concept(s) générique(s)

triangle center

Concept(s) associé(s)

triangle

Synonyme(s)

Jacobi point

Traductions

théorème de Jacobi

français
point de Jacobi
théorème de Fermat-Toricelli généralisé
théorème isogonal

URI

http://data.loterre.fr/ark:/67375/PSR-D1LDBSDF-L

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RDF/XML TURTLE JSON-LD Date de création 11/08/2023, dernière modif. 11/08/2023