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Given a ΔABC, let R, r, ra, rb, rc be the radii of the circumcircle (O), the incircle (I) and the excircles (Ia), (Ib) and (Ic). The fourth tangents common to pairs of the excircles (Ia), (Ib) and (Ic) form a triangle A'B'C'. Show that centers of the incircle of ΔA'B'C' and the circumcircle of ΔIaIbIc coincide and that the radius r' of the former satisfies:
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r' = 2R + r = (r + ra + rb + rc)/2.
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