Jacobi's theorem (geometry)

In plane geometry, a Jacobi point is a point in the Euclidean plane determined by a triangle △ABC and a triple of angles α, β, γ.

Then, by a theorem of Karl Friedrich Andreas Jacobi [de], the lines AX, BY, CZ are concurrent,[1][2][3] at a point N called the Jacobi point.

[3] The Jacobi point is a generalization of the Fermat point, which is obtained by letting α = β = γ = 60° and △ABC having no angle being greater or equal to 120°.

If the three angles above are equal, then N lies on the rectangular hyperbola given in areal coordinates by

Each choice of three equal angles determines a triangle center.