The dynamic geometry figure below shows four green circles c1, c2, c3, and c4 passing through a point P. Circles c1 and c2 intersect at P12, and so on, P13, P23, P24, P14, and P34. Red Circle c123 passes through P12, P23, and P13, and so on. Prove that the four red circles pass through a point M.
	     
 

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		Ten problems: 1411-1420
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        	Circle
						                
  						
						
			Intersecting Circles
						                
  						
			
			Classical Theorems
                
		                
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