MathNet 2016-part-01 — 184 problems (EN–VI) Question 82

Let $ABCD$ be a convex quadrilateral. Let $P$ be a point such that $\angle APC = \angle BPD = 30^\circ$. Prove that
$$
2(AB + AC + AD + BC + BD + CD) \geq PA + PB + PC + PD.
$$