one of the line is parallel to the euler line
Source: India tst 2003, p4
March 13, 2012
Eulergeometry unsolvedgeometry
Problem Statement
There are four lines in the plane, no three concurrent, no two parallel, and no three forming an equilateral triangle. If one of them is parallel to the Euler line of the triangle formed by the other three lines, prove that a similar statement holds for each of the other lines.