Let ABC be an arbitrary triangle with circumradius R, incenter I, and inradius r.
Let I_A, I_B, and I_C be the excenters of ABC lying on the bisectors of interior angles A, B, and C respectively.

What is the value of the following product of ratios ?

    |IIA|     |IIB|     |IIC|      r
   ------- x ------- x ------- x ---
    |IA|      |IB|      |IC|      R