In the figure below, ABC is a triangle
inscribed in a circle of center O (circumcenter), I is the
incenter and
E_{1}, E_{2}, E_{3} are the excenters relatives to the sides BC,
AC, and AB respectively. If R, is the circumradius, d = OI, d_{1}
= OE_{1},
d_{2}
= OE_{2},
and d_{3}
= OE_{3}, prove that
.
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