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Geometry Problem 1302: Triangle, Median, Circles, Midpoint, Congruence. Level: School, College, Mathematics Education

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The figure below shows a triangle ABC with the median BM. D is a point on AC. Circle of diameter AD cuts BD at E and circle of diameter DC cuts BD extended at F. Prove that ME = MF.
 

Geometry Problem 1302: Triangle, Median, Circles, Diameters, Congruence
  
 

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