proof of trigonometric version of Ceva’s theorem

The proof goes by proving the condition imposed on the sines, is equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath to the one imposed on the sides on the normal version of Ceva’s theorem.

We want to prove


if and only if


Now, the generalization of bisectors theorem states that


Multiplying the three equations, and cancelling all segments on the right side gives the desired equivalence.

Title proof of trigonometric version of Ceva’s theorem
Canonical name ProofOfTrigonometricVersionOfCevasTheorem
Date of creation 2013-03-22 14:49:20
Last modified on 2013-03-22 14:49:20
Owner drini (3)
Last modified by drini (3)
Numerical id 7
Author drini (3)
Entry type Proof
Classification msc 51A05