Use the following steps to construct a figure.[br][list=1][*]Pick non-collinear points A, B, C [note: you can move any of these points][br][/*][*]Pick point M inside triangle A.B.C [note: you can move point M][/*][*]Locate point M_c such that quadrilateral A.M.B.M_c is a parallelogram.[br][/*][*]Locate point M_b such that quadrilateral A.M.C.M_b is a parallelogram.[/*][*]Locate point M_a such that quadrilateral B.M.C.M_a is a parallelogram. [/*][/list][br]Examine line segments A.M_a, B.M_b, C.M_c --- are they related in any special fashion?

[i]The Generalized Conception in Problem Solving[/i], A. V. Brushlinskii,[br][i]Analyses of Reasoning Processes[/i], pages 45--55