Ceva's theorem


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Ceva's theorem

[′chā·vəz ‚thir·əm]
(mathematics)
The theorem that if three concurrent straight lines pass through the vertices A, B, and C of a triangle and intersect the opposite sides, produced if necessary, at D, E, and F, then the product AF·BD·CE of the lengths of three alternate segments equals the product FB·DC·EA of the other three.
References in periodicals archive ?
If we use the Ceva's theorem in the gyrotriangle ABC (See Theorem 1), we have
But the last fraction is equal to 1 in conformity to Ceva's theorem.
Here you will find proof strategies including proofs of Ceva's Theorem and Jacobi's Theorem and examples of how one result in concurrency can be used to prove others.