escribed circles

Given a triangle, extend two sides in the direction opposite their common vertex. The circle tangent to these two lines and to the other side of the triangle is called an excircle, or sometimes an escribed circle. The center J_i of the excircle is called the excenter and lies on the external angle bisector of the opposite angle. Every triangle has three excircles, and the trilinear coordinates of the excenters are -1:1:1, 1:-1:1, and 1:1:-1. The radius r_i of the excircle i is called its exradius. Note that the three excircles are not necessarily tangent to the incircle, and so these four circles are not equivalent to the configuration of the Soddy circles. No Kimberling centers lie on any of the excircles.

excenter | excenter-excenter circle | excentral triangle | excircles radical circle | exradius | extangents triangle | Feuerbach's theorem | Feuerbach triangle | Nagel point | triangle transformation principle