High Quality Content by WIKIPEDIA articles! In geometry, the isotomic lines of a point in relation to a triangle are the cevians through the point from each polygon vertex which meet the opposite sides. The isotomic conjugate can be constructed from the iscotomic lines. In geometry, the isotomic conjugate of a point P not on a sideline of triangle ABC is constructed as follows: Let A', B', C' be the points in which the lines AP, BP, CP meet the lines BC, CA, AB, respectively. Reflect A'B'C' in the midpoints of sides BC, CA, AB to obtain points A", B", C", respectively. The lines AA", BB", CC" meet at a point (this can be proved using Ceva's theorem), and this point is called the isotomic conjugate of P.

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