 In a triangle "ABC" with sides "a", "b", and "c", where the vertices are labeled "A", "B" and "C" in counterclockwise order, there is exactly one point "P" such that the line segments "AP", "BP", and "CP" form the same angle, ω, with the respective sides "c", "a", and "b", namely that

Point "P" is called the first Brocard point of the triangle "ABC", and the angle "ω" is called the Brocard angle of the triangle.This angle has the property that

where formula_3 are the vertex angles formula_4 respectively.There is also a second Brocard point, Q, in triangle "ABC" such that line segments "AQ", "BQ", and "CQ" form equal angles with sides "b", "c", and "a" respectively.