The figure shows a triangle ABC with orthocenter H. AT is tangent to the 
	  circle with diameter BC, TH extended meets the circle at F. If AH = 20, 
	  HE = 7, and TH = 16, find the measure of HF.
The orthocenter of a triangle is the point of intersection of the altitudes.
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        	Triangle
 
			
			Altitude
 
			
			Orthocenter
	  
				Perpendicular lines
			Circle
		
						Diameter
						                
  						
        Circle Tangent Line
						                
  						
			Triangle Centers
         
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