Isoperimetric point

In geometry, the isoperimetric point is a special point associated with a plane triangle. The term was originally introduced by G.R. Veldkamp in a paper published in the American Mathematical Monthly in 1985 to denote a point P in the plane of a triangle ABC having the property that the triangles PBC, PCA and PAB have isoperimeters, that is, having the property that PB + BC + CP = PC + CA + AP = PA + AB + BP. ( sec ( A/2 ) cos ( B/2 ) cos ( C/2 ) − 1 , sec ( B/2 ) cos ( C/2 ) cos ( A/2 ) − 1 , sec ( C/2 ) cos ( A/2 ) cos ( B/2 ) − 1 )

Isoperimetric point

In geometry, the isoperimetric point is a special point associated with a plane triangle. The term was originally introduced by G.R. Veldkamp in a paper published in the American Mathematical Monthly in 1985 to denote a point P in the plane of a triangle ABC having the property that the triangles PBC, PCA and PAB have isoperimeters, that is, having the property that PB + BC + CP = PC + CA + AP = PA + AB + BP. ( sec ( A/2 ) cos ( B/2 ) cos ( C/2 ) − 1 , sec ( B/2 ) cos ( C/2 ) cos ( A/2 ) − 1 , sec ( C/2 ) cos ( A/2 ) cos ( B/2 ) − 1 )