Given : ABCD is a rhombus with AB = 12 cm and $$angle$$ ABC = 120° To find : AC = ? Solution : Diagonals of a rhombus bisect each other at 90° and bisect the angles opposite to them. => $$angle$$ OBA = 60° In $$ riangle$$ AOB, $$sin (angle OBA) = frac{OA}{AB}$$ => $$sin(60) = frac{OA}{12}$$ => $$frac{sqrt{3}}{2} = frac{OA}{12}$$ => $$OA = 6sqrt{3}$$ cm Since, the diagonals bisect each other, => $$AC = 2 imes (OA)$$ = $$2 imes 6sqrt{3} = 12sqrt{3}$$ cm => Ans - (D)