The figure below shows a triangle ABC with the circumradius R, the inradius r and the exradii ra, rb, rc. Prove that \(r_a+r_b+r_c=4 \cdot R+r\) .
	     
 

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        	Triangle
              
		                
			Circle
						                
  						
			Triangle Centers
 
			
			Circumradius, Circumcenter
 
			
			Inradius, Incenter, Incircle
               
		
			
			Exradius, Excenter, Excircle
 
               
		
									Circle Tangent Line
 
               
		
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