SHOW THAT THE CIRCUMRADIUS R OF A TRIANGLE ABC EQUALS THE ARITHMETI...
1. Show that the circumradius R of a triangle ABC equals the arithmetic mean of the oriented
distances from its incenter I and three excenters I
a
; I
b
; I
c
to any tangent τ to its circumcircle. In
other words, if δ(P ) denotes the distance from a point P to τ ; then with appropripriate choices
of signs, we have
δ(I) ± δ(I
a
) ± δ(I
b
) ± δ(I
c