Orthopole

In geometry, the orthopole of a system consisting of a triangle ABC and a line ℓ in the same plane is a point determined as follows.

[1] Let A ′, B ′, C ′ be the feet of perpendiculars dropped on ℓ from A, B, C respectively.

[2] The point at which they concur is the orthopole.

Due to their many properties,[3] orthopoles have been the subject of a large literature.

[4] Some key topics are determination of the lines having a given orthopole[5] and orthopolar circles.