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collinear wanted, segments with collinear midpoints given, AX//BY// CZ// \ell.

Source: Mathley 2014.1 p1

August 19, 2020
geometrycollinearmidpointparallel

Problem Statement

Let AD,BE,CFAD, BE, CF be segments whose midpoints are on the same line ℓ\ell. The points X,Y,ZX, Y, Z lie on the lines EF,FD,DEEF, FD, DE respectively such that AX∥BY∥CZ∥ℓAX \parallel BY \parallel CZ \parallel \ell. Prove that X,Y,ZX, Y, Z are collinear.
Tran Quang Hung, High School of Natural Sciences, Hanoi National University
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