Question 7
(CHN 2) Let $O$ be the center of the circumsphere of a tetrahedron $ABCD$. Let $L,M,N$ be the midpoints of $BC,CA,AB$ respectively, and assume that $AB+BC=AD+CD$, $BC+CA=BD+AD$, and $CA+AB=CD+BD$. Prove that $\angle LOM=\angle MON=\angle NOL$.