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

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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 \((2+\sqrt{2}):6\)

OA C

Source: Princeton Review