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Another center of mass problem

Source: Romanian National Olympiad 2014, Grade IX, Problem 3

March 2, 2019
geometrycenter of massanalytic geometry

Problem Statement

Let P,Q P,Q be the midpoints of the diagonals BD, BD, respectively, AC, AC, of the quadrilateral ABCD, ABCD, and points M,N,R,S M,N,R,S on the segments BC,CD,PQ, BC,CD,PQ, respectively AC, AC, except their extremities, such that BMMC=DNNC=PRRQ=ASSC. \frac{BM}{MC}=\frac{DN}{NC}=\frac{PR}{RQ}=\frac{AS}{SC} . Show that the center of mass of the triangle AMN AMN is situated on the segment RS. RS.
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