Geometry Problem 1383: Triangle, Median, Circle, Chord, Secant, Sum, Product

Proposition

The figure below shows a triangle ABC with the median BM. A circle O passing through the vertex B intersects AB, CB, and MB at points D, E, and F, respectively. Prove that a.e + c.d = 2m.f
 

Geometry Problem 1383: Triangle, Median, Circle, Secant, Sum, Product
 

See also
Conformal Mapping or Transformation of Problem 1382

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