In a scalene triangle ABC, D is the foot of the altitude through A, E is the intersection of AC with the bisector of ∠ABC and F is a point on AB. Let O the circumcenter of ABC and X=AD∩BE, Y=BE∩CF, Z=CF∩AD. If XYZ is an equilateral triangle, prove that one of the triangles OXY, OYZ, OZX must be equilateral. geometrycircumcirclegeometric transformationreflectiongeometry proposed