Given a point P in the interior of a triangle Δ A_1 A_2 A_3, draw the cevians through P from each polygon vertex which meet the opposite sides at P_1, P_2, and P_3. Now, mark off point Q_1 along side A_2 A_3 such that A_3 P_1 = A_2 Q_1, etc., i.e., so that Q_i and P_i are equidistance from the midpoint of A_j A_k. The lines A_1 Q_1, A_2 Q_2, and A_3 Q_3 then coincide in a point Q known as the isotomic conjugate.
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