Let r be a line, ra the reflection in BC of the parallel to r through A. Define analogously rb, rc. The lines ra, rb, rc bound a triangle and the reflection of this triangle in r is homothetic to ABC with ratio 3. When r is the Euler line the homothetic center is X(125); when r is the line OI (O circumcenter, I incenter) the homothetic center is the Feuerbach point.