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              In the figure below, the circles of 
				centers O and A are tangent at B, the circles O and F are 
				tangent at G. A chord CD of the circle O is tangent to the 
				circle A at E and tangent to the circle F at H. GH and BE meet 
				at a point M. Prove that M is the midpoint of arc CD.   
				
				  
				
				  
				  
				  
                
  
						Flyer of problem 54 using iPad Apps
							  												
	   
				 
				
				
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				Problem 53 
						
				
						 
              I have used
				Geometry Expressions to visualize these geometric forms and 
				check out a variety of conjectures. Geometry Expressions is the 
				world's first Interactive Symbolic Geometry System. This means: 
				Geometric figures can be defined by either Symbolic Constraints 
				or numeric locations. 
				 
  
						
  
    				
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	Spanish Problem 54 |
	
	51-60 |
									Circle Tangent Line |
	Email | By Antonio Gutierrez
  
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	54  |