geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, the orthopole of a system consisting of a

triangle A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, an ...

''ABC'' and a line ''ℓ'' in the same plane is a point determined as follows. Let be the feet of perpendiculars dropped on ''ℓ'' from respectively. Let be the feet of perpendiculars dropped from to the sides opposite (respectively) or to those sides' extensions. Then the three lines are

concurrent Concurrent means happening at the same time. Concurrency, concurrent, or concurrence may refer to: Law * Concurrence, in jurisprudence, the need to prove both ''actus reus'' and ''mens rea'' * Concurring opinion (also called a "concurrence"), a ...

. 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

References

{{Reflist Points defined for a triangle