The figure below shows circles O_{1} and
O_{2} with the secants C_{1}AC_{2}, D_{1}AD_{2},
and E_{1}AE_{2}. D_{1}C_{1} and C_{2}D_{2} meet at F;
E_{1}D_{1} and D_{2}E_{2}
meet at G.
If O_{3}, O_{4}, and O_{5} are the
circumcenters of triangles C_{1}C_{2}F, D_{1}D_{2}F,
and E_{1}E_{2}G, respectively, prove that the points
O_{1}, B, O_{2}, O_{3}, O_{4},
and O_{5} are concyclic.
