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Some geo

Source: flanders junior olympiad '05

April 25, 2005
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Problem Statement

(a) Be M an internal point of the convex quadrilateral ABCD. Prove that ∣MA∣+∣MB∣<∣AD∣+∣DC∣+∣CB∣|MA|+|MB| < |AD|+|DC|+|CB|. (b) Be M an internal point of the triangle ABC. Note k=min⁡(∣MA∣,∣MB∣,∣MC∣)k=\min(|MA|,|MB|,|MC|). Prove k+∣MA∣+∣MB∣+∣MC∣<∣AB∣+∣BC∣+∣CA∣k+|MA|+|MB|+|MC|<|AB|+|BC|+|CA|.
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