Distance between Excenters of Triangle in Terms of Circumradius

Theorem
Let $\triangle ABC$ be a triangle whose sides are $a$, $b$ and $c$ opposite vertices $A$, $B$ and $C$ respectively.

Let $I_a$ and $I_b$ be the excenters of $\triangle ABC$ $a$ and $b$ respectively.

Let $R$ be the circumradius of $\triangle ABC$.

Then:
 * $I_a I_b = 4 R \cos \dfrac C 2$