Integer Triangle of the Gergonne Point
A rational triangle has all three sides rational numbers, and a rational point with respect to a triangle means that the distances from to the vertices of are rational.[more]
If and are rational and , it is possible to construct a rational triangle based on these values such that the Gergonne point is a rational point of .
Then we have:
According to the rational isogonal conjugates theorem, since is a rational point of , so is its isogonal conjugate .[less]
 C. Kimberling. "Encyclopedia of Triangle Centers." (Dec 29, 2022) faculty.evansville.edu/ck6/encyclopedia.