Given:  

$ \triangle ABC $  

$AC = BC$  

$\angle C = 150$  

$AB (base) = \sqrt{12}$  

Find the radius of the Circumcircle.  

I have no idea how to solve this challenge, the answer which is given in the textbook is $2\sqrt{3}$ (which is the base).

**P.S.** The textbook is for 8th grade, and in my country, sin and cosine law are learned in 9th grade(next year). So proofs without trigonometry are preferred.