The Gergonne point Ge is the perspector of a triangle Δ A B C and its contact triangle Δ T_A T_B T_C. It has equivalent triangle center functions α | = | [a(b + c - a)]^(-1) α | = | sec^2(1/2 A) and is Kimberling center X_7. The Gergonne point Ge is the isotomic conjugate of the Nagel point Na. The Gergonne point of a triangle is the symmedian point of its contact triangle. The Gergonne point G e, triangle centroid G, and mittenpunkt M are collinear, with G e G:G M = 2:1.

Adams' circle | contact triangle | Gergonne line | Nagel point

Joseph Diaz Gergonne