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. Let A, B, C be the feet of perpendiculars dropped on ℓ from A, B, C respectively. Let A, B, C be the feet of perpendiculars dropped from A, B , C to the sides opposite A, B, C (respectively) or to those sides' extensions. Then the three lines A A, B B, C  C , are concurrent. The point at which they concur is the orthopole.

Due to their many properties, orthopoles have been the subject of a large literature. Some key topics are determination of the lines having a given orthopole and orthopolar circles.

Literature

 * Orthopole=Ортополюс. In Russian