Suppose that $A, B, C$, and $X$ are any four distinct points in the plane with $$\max \,(BX,CX) \le AX \le BC.$$Prove that $\angle BAC \le 150^o$.
Problem
Source: 2015 Baltic Way Shortlist G7 BW https://artofproblemsolving.com/community/c2641329_baltic_way_shortlist__geometry
Tags: angles, geometric inequality, geometry