Posts tagged 'inquadrance'

W.12 Vertex Bisectors, Square Vertices & The Four Incenters

The locus of points X having equal quadrance Q(X, l_1) = Q(X, l_2) to two intersecting non-null lines l_1, l_2 splits into two orthogonal vertex bisectors over F if and only if (a_1^2 + b_1^2)(a_2^2 + b_2^2) is a square in F; when two vertices of a triangle have bisectors in F, so does the third, producing four symmetric incenters I_0, I_1, I_2, I_3.