There exist two points P and Q in the plane of the triangle
Source:
October 7, 2010
geometrycircumcirclegeometric transformationreflectiongeometry proposed
Problem Statement
Let be a nonequilateral triangle. Prove that there exist two points and in the plane of the triangle, one in the interior and one in the exterior of the circumcircle of , such that the orthogonal projections of any of these two points on the sides of the triangle are vertices of an equilateral triangle.