Posts tagged 'excircle'

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.48 Verisimilitude, Corner Subtriangles, and Excircle Homothety

If lines parallel to the sides of triangle ABC are drawn tangent to the incircle, the three corner subtriangles are homothetic to ABC with scale factors x/s, y/s, z/s (where x = s - a, y = s - b, z = s - c), so their inradii satisfy r_A + r_B + r_C = r.