Let Ab, Ac lbe the contact points between the circumcircle and the common tangents to it and the A-excircle. Define analogously Bc, Ba, Ca, Cb. The excenters Eb, Ec are concyclic with Ab, Ac. The same happens with the other two pairs. Let Xa, Xb, Xc the centers of the three circles. The lines AXa, BXb, CXc concur at the point X(84).