Gergonne point

Named after Joseph Diaz Gergonne.

Gergonne point (plural Gergonne points)

1. (geometry) A certain triangle center. Given a triangle ${\displaystyle \triangle ABC}$ and its Gergonne triangle (with the touchpoint opposite ${\displaystyle A}$ denoted by ${\displaystyle T_{A}}$, etc.), the Gergonne point is the intersection of the three lines ${\displaystyle AT_{A}}$, ${\displaystyle BT_{B}}$, and ${\displaystyle CT_{C}}$.