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		The diagram shows a triangle ABC with the 
		altitude BD. E is on BD and F is on BD extended such that DE = DF. The 
		circumcircle of triangle AEF meets AB and AC at N and G, respectively. 
		The circumcircle of triangle CEF meets BC and AC at M and H, 
		respectively. Prove that BF, MH, and NG are concurrent.
 
				  
 
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