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| <PAB - <PAC| >= |<PBC - <PCB| in equilateral (HOMC 2017 Q11)

Source:

August 3, 2019
geometryinequalitiesgeometric inequalityanglesEquilateral

Problem Statement

Let ABCABC be an equilateral triangle, and let PP stand for an arbitrary point inside the triangle. Is it true that ∣∠PAB−∠PAC∣≥∣∠PBC−∠PCB∣| \angle PAB - \angle PAC| \ge | \angle PBC - \angle PCB| ?
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