Prove concyclic

Join BE and CD and let ∠BDC = θ and ∠BDA = α as follows:




圖片參考：http://i1191.photobucket.com/albums/z467/robert1973/May13/Crazy20_zps39f5c5eb.jpg
Then we have:

∠BEC = ∠DAC = ∠CAB = θ since arc BC = arc CD

∠BEA = ∠BDA = α (Angle in the same segment)

So ∠DPC = θ + α (Ext. ∠ of triangle)

Also with ∠AEQ = θ + α = ∠DPC, A, P, Q and E are concyclic.