Posts tagged 'euler-formula'

F.20 Extangent

The external common tangents to the incircle and circumcircle (or excircles) bound the extangents triangle, while Euler’s relation d_{IO}^2 = R^2 - 2rR has derivative d(d_{IO})/dR = (R - r)/sqrt(R^2 - 2rR).

F.28 Incenter

The three interior angle bisectors of triangle ABC concur at the incenter I = X(1) with homogeneous barycentric coordinates a : b : c, inradius r = K/s satisfying 1/r = 1/h_a + 1/h_b + 1/h_c, and Euler’s distance d_{IO}^2 = R(R - 2r).