What is the area of the circle with center \(C,\) shown above?


(1) The ratio of the area of the region enclosed by segment \(AC,\) segment \(CB,\) and minor arc \(AB\) to the area of triangle \(ABC\) is equal to the ratio of the ratio of half the area of circle \(C\) to the area of triangle \(ABD.\)

(2) The ratio of the perimeter of triangle \(ABC\) to the area of triangle \(ACD\) is \((2+\sqrt2):6.\)

Answer: C

Source: Princeton Review