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Romania District Olympiad 2001 - Grade IX

Source:

March 12, 2011
geometry proposedgeometry

Problem Statement

In the xOyxOy system consider the lines d1 : 2x−y−2=0, d2 : x+y−4=0, d3 : y=2d_1\ :\ 2x-y-2=0,\ d_2\ :\ x+y-4=0,\ d_3\ :\ y=2 and d4 : x−4y+3=0d_4\ :\ x-4y+3=0. Find the vertices of the triangles whom medians are d1,d2,d3d_1,d_2,d_3 and d4d_4 is one of their altitudes.
Lucian Dragomir
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