Let I be the incenter of ΔABC.

Let A', B', and C' be the circumcenters of ΔIBC, ΔICA. and ΔIAB.

Prove the following:

   A) For each X ∈ {A,B,C} ( line XI intersects the circumcircle of
        ΔABC again at X' ).

   B) Area(ΔA'B'C') / Area(ΔABC) = R / 2r, where R and r are the

         circumradius and inradius of ΔABC respectively.