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triangle, parallelograms, incidence

Dick Lane
Use the following steps to construct a figure.
  1. Pick non-collinear points A, B, C [note: you can move any of these points]
  2. Pick point M inside triangle A.B.C [note: you can move point M]
  3. Locate point M_c such that quadrilateral A.M.B.M_c is a parallelogram.
  4. Locate point M_b such that quadrilateral A.M.C.M_b is a parallelogram.
  5. Locate point M_a such that quadrilateral B.M.C.M_a is a parallelogram.
Examine line segments A.M_a, B.M_b, C.M_c --- are they related in any special fashion?
The Generalized Conception in Problem Solving, A. V. Brushlinskii, Analyses of Reasoning Processes, pages 45--55