O is the center (given) and CO therefor is the circle radii R = 6 - statement (1).
The arc BC is 2 pi long (given) - statement (2).
circumference of the circle is 2Rpi = 12pi
the ratio of BC / circumference is 2 / 12
2 / 12 * 360 = 60
we can now tell that BOC = 60 degrees
so my answer is (C)
I didn't gave any weight to AD = AE - is that correct ?