The isotomic conjugate can be constructed from the iscotomic lines.

It is the isotomic conjugate of the Gergonne point.

The isotomic conjugate of the centroid of triangle ABC is the centroid itself.

In geometry, the isotomic conjugate of a point P with respect to a triangle ABC is another point, defined from P and ABC.

Isotomic conjugates of lines are circumconics, and conversely, isotomic conjugates of circumconics are lines.

The isotomic lines AA", BB" and CC" joining these new points to the vertices meet at a point (which can be proved using Ceva's theorem), the isotomic conjugate of P.