Semmedia

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by coil0187 July 10, 2025

See median, draw symmedian

A little known trick which solves every single geometry problem in existence. It is used through drawing the isogonal conjugate of a median in a triangle after observing a median, and usually allows the use of Desargues' involution theorem to instantly finish the problem.

"How do you solve this problem?"
"See median, draw symmedian"

by xor2004 July 15, 2023

Symmedian Point

Given a triangle, construct its circumcircle and the tangents on each corner. Connect the intersections of the tangents to the opposite triangle vertice to form a symmedian.

The three symmedians coincide at the Symmedian Point, which is a reflection of the Incenter about the relevant median(s)

The Symmedian point is an important part of geometry

by obama sussy hamburger January 11, 2023