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 Problem 54. Tangent Circles, angle bisector, midpoint. Level: High School, SAT Prep, College

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.
 

 

Angles, Tangent Circles, Arc, Midpoint
 
 

  Hints: See 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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