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In the figure, ABC is an equilateral triangle, and DAB is a right triangle. What is the area of the circumscribed circle?
(1) DA = 4
(2) Angle ABD = 30 degrees
In the original condition, the angle of circumference is identical and Angle ADB = 60 degrees.(Since triangle ABC is equilateral and angle C is 60 degrees , angle C = angle ADB). And since the central angle is double the angle of circumference, DB is the diameter. Then, since with particular angles DB = 2DA (1:root3:2), we only need to find out DA and since we have 1 variable, D is likely the answer. (We get the answer once we match the number of equations and number of variables. condition (1) & (2) have 1 each, thus D is likely the answer.)
In case of (1), DB=8 makes it sufficient, but (1) is just a replicate of the original condition, thus it is not sufficient. Therefore the answer is A.
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