TR-MO-R1 2009 Problem 17

$ABC$ eşkenar üçgeninin iç bölgesindeki bir $D$ noktası, $|AD| = 8$ , $|BD| = 13$ ve $m(\widehat{ADC}) = 120^o$ koşullarını sağlıyorsa $|DC|$ kaçtır?

a) $12$ b) $13$ c) $14$ d) $15$ e) $16$

Official text Turkish Mathematical Olympiad, first round 2009 official paper, page 6. Quoted with source.

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