TR-MO-R1 2010 Problem 5

Dışbükey bir $ABCD$ dörtgeninde, $|AB| = 10$, $|CD| = 3\sqrt{6}$, $m(\widehat{ABD}) = 60^o$, $m(\widehat{BDC}) = 45^o$, $|BD| = 13 + 3\sqrt{3}$ ise, $|AC|$ kaçtır?

a) $20$ b) $18$ c) $16$ d) $14$ e) $12$