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< BAC <=150^o if max (BX,CX) <= AX <= BC

Source: 2015 Baltic Way Shortlist G7 BW https://artofproblemsolving.com/community/c2641329_baltic_way_shortlist__geometry

November 23, 2021
anglesgeometric inequalitygeometry

Problem Statement

Suppose that A,B,CA, B, C, and XX are any four distinct points in the plane with max⁡ (BX,CX)≤AX≤BC.\max \,(BX,CX) \le AX \le BC. Prove that ∠BAC≤150o\angle BAC \le 150^o.
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