TR-MO-R1 2011 Problem 1

Aşağıdakilerden hangisi, $[AB]$ ve $[CD]$ kenarlarının orta dikmeleri $[AC]$ köşegeni üstündeki bir noktada kesişen her $ABCD$ dışbükey dörtgeni için doğrudur?

a) $|BA|+|AD| \leq |BC|+|CD|$ b) $|BD| \leq |AC|$ c) $|AC| \leq |BD|$

d) $|AD|+|DC| \leq |AB|+|BC|$ e) Hiçbiri

Official text Turkish Mathematical Olympiad, first round 2011 official paper, page 2. Quoted with source.

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