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Geometric inequality

Source: China South East Mathematical Olympiad2011

August 18, 2011
inequalitiesvectorinequalities proposed

Problem Statement

Let PiP_i i=1,2,......ni=1,2,......n be nn points on the plane , MM is a point on segment ABAB in the same plane , prove : ∑i=1n∣PiM∣≤max⁡(∑i=1n∣PiA∣,∑i=1n∣PiB∣)\sum_{i=1}^{n} |P_iM| \le \max( \sum_{i=1}^{n} |P_iA| , \sum_{i=1}^{n} |P_iB| ). (Here ∣AB∣|AB| means the length of segment ABAB) .
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