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|AM | -|PM| >= d fon any M \in BC (HOMC 2017 Q13)

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August 3, 2019
inequalitiesdistanceGeometric Inequalitiesgeometry

Problem Statement

Let ABCABC be a triangle. For some d>0d>0 let PP stand for a point inside the triangle such that ∣AB∣−∣PB∣≥d|AB| - |P B| \ge d, and ∣AC∣−∣PC∣≥d|AC | - |P C | \ge d. Is the following inequality true ∣AM∣−∣PM∣≥d|AM | - |P M | \ge d, for any position of M∈BCM \in BC ?
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