Orthopole
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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. 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.[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.[6]