An isosceles triangle ABC with AB=AC and ∠A=30o is inscribed in a circle with center O. Point D lies on the shorter arc AC so that ∠DOC=30o, and point G lies on the shorter arc AB so that DG=AC and AG<BG. The line BG intersects AC and AB at E and F, respectively.
(a) Prove that triangle AFG is equilateral.
(b) Find the ratio between the areas of triangles AFE and ABC. isoscelesEquilateraltriangle areaarea