Let Aa, Ba, Ca the contact points between the A-excircle and the sides. Define analogously Ab, Bb, Cb, Ac, Bc, Cc. Let A', B', C' be the vertices of the intouch triangle. Then the points C', A', Cb, Ab are concyclic, lying in a circle centered at the midpoint between the incenter I and the excenter EB, and the lines C'Ab, A'Cb, BI concur.