Set of Simson Lines
Source: Turkey Team Selection Test 2018 P9
March 27, 2018
geometrySimson Lines
Problem Statement
For a triangle and a line , if the feet of perpendicular lines from a point in the plane to the edges of all lie on , say focuses . If the set of lines focusing and the set of lines focusing are the same, say and are equivalent. Prove that, for any triangle in the plane, there exists exactly one equilateral triangle which is equivalent to it.