Distance between Incenter and Excenter 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 $I$ be the incenters of $\triangle ABC$.

Let $I_a$ be the excenters of $\triangle ABC$ $a$.

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

Then:
 * $I I_a = 4 R \sin \dfrac A 2$