Posts tagged 'orthic triangle'

W.15 Circumcenter, Orthocenter & Universal Affine Barycentrics

Every non-null triangle A_1 A_2 A_3 over a field F (char F != 2) has a unique circumcenter C at the intersection of its side perpendicular bisectors and a unique orthocenter O at the intersection of its altitudes, with affine barycentric weights beta_i = Q_i*(Q_j + Q_k - Q_i)/(2*A) for C and gamma_i = (Q_i + Q_j - Q_k)*(Q_k + Q_i - Q_j)/(2*A) for O.