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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. Prove that the points B, D_{1}, G, F, and D_{2} are concyclic.

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