Isotomic Conjugate
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.