High Quality Content by WIKIPEDIA articles! 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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