Cevian line: Difference between revisions
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imported>Richard Pinch (→Concurrent sets: add angle bisectors) |
imported>Richard Pinch (References: Coxeter+Greitzer) |
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* The [[median (geometry)|median]]s | * The [[median (geometry)|median]]s | ||
* The angle bisectors | * The angle bisectors | ||
==References== | |||
* {{cite book | author=H.S.M. Coxeter | coauthors=S.L. Greitzer | title=Geometry revisited | series=New Mathematical Library | volume=19 | publisher=[[MAA]] | year=1967 | isbn=0-88385-619-0 }} |
Revision as of 17:31, 24 November 2008
In triangle geometry, a Cevian line is a line in a triangle joining a vertex of the triangle to a point on the opposite side. A Cevian set is a set of three lines lines, one for each vertex. A Cevian set is concurrent if the three lines meet in a single point.
Ceva's theorem
Let the triangle be ABC, with the Cevian lines being AX, BY and CZ. Ceva's theorem states that the Cevian set is concurrent if and only if
Concurrent sets
Examples of concurrent Cevian sets include:
References
- H.S.M. Coxeter; S.L. Greitzer (1967). Geometry revisited. MAA. ISBN 0-88385-619-0.