radiation symbol theorem

A parallelian is a line drawn parallel to one side of a triangle. The three lines drawn through a given point are known as the triangle's parallelians. There exists a unique point in the interior of a triangle that results in three parallelians of equal length. This point is known as the equal parallelians point. There is a beautiful theorem connecting the areas of the three triangles determined by parallelians with the area Δ of the reference triangle.

equal parallelians point | Lemoine hexagon | Thomsen's figure | triangulation point | Tucker circles