The inscribed circle of triangle ABC is tangent to sides BC, AC and AB at points D, E and F, respectively. Let E′ be the reflection of point E across line DF, and F′ be the reflection of point F across line DE. Let line EF intersect the circumcircle of triangle AE′F′ at points X and Y. Prove that DX=DY.Proposed by Márton Lovas, Budapest geometrycircumcirclegeometric transformationreflectionkomal