Problem

Source: Iran Third Round 1997, E1, P2

Tags: geometry, parallelogram, geometric transformation, rotation, geometry unsolved



Let $ABCD$ be a parallelogram. Construct the equilateral triangle $DCE$ on the side $DC$ and outside of parallelogram. Let $P$ be an arbitrary point in plane of $ABCD$. Show that \[PA+PB+AD \geq PE.\]