TR-MO-R1 2012 Problem 9

$[AB]$ çaplı çemberin $[CD]$ kirişi $[AB]$ ye diktir. $M$ ve $N$ sırasıyla, $[BC]$ ve $[AD]$ nin orta noktaları olmak üzere, $|BC| = 6$ ve $|AD| = 2\sqrt{3}$ ise, $|MN|$ nedir?

a) $4$ b) $3\sqrt{2}$ c) $\sqrt{21}$ d) $5$ e) Hiçbiri

Official text Turkish Mathematical Olympiad, first round 2012 official paper, page 4. Quoted with source.

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