(a) \(\frac{3}{\sqrt{3}}(\frac{2}{\sqrt{3}} - \frac{\sqrt{12}}{6})\) = \(\frac{6}{\sqrt{9}} - \frac{3\sqrt{12}}{6\sqrt{3}}\) = \(2 - \frac{2\sqrt{3}}{2\sqrt{3}}\) = \(2 - 1 = 1\) (b)(i) \(< ABC = 180^\circ - 68^\circ = 112^\circ\) \(< AOC = 2 \times 112^\circ = 224^\circ\) \(\hat{O} = < AOC (obtuse)\) = \(360^\circ - 224^\circ = 136^\circ\) (ii) In \(\Delta AOC\), OA = OC (radii) \(\therefore \Delta AOC = isosceles\) \(\hat{A} = < OAC ; \hat{C} = < ACO ; \hat{A} = \hat{C} = x\) \(\hat{O} + \hat{A} + \hat{C} = 180^\circ\) \(136^\circ + x + x = 180^\circ \implies 2x = 44^\circ\) \(x = 22^\circ\) In \(\Delta BOC\), OB = OC (radii) \(\therefore \Delta BOC = isosceles\) \(< OCB = 49^\circ + 22^\circ= 71^\circ\) \(< OBC = < OCB = 71^\circ\) \(< OBC + < OCB + < BOC = 180^\circ\) \(71^\circ + 71^\circ + < BOC = 180^\circ\) \(< BOC = 180^\circ - 142^\circ = 38^\circ\)