In △ ABC, the angular bisectors AE and be of ∠ BAC and ∠ ABC intersect at point E, extend the circumscribed circle of AE intersecting △ ABC at point D, connect BD, CD and CE, and ∠ BDA = 60 ° ① prove that △ BDE is an equilateral triangle; ② guess what kind of quadrilateral bdce is if ∠ BDC = 120 ° and prove your guess; ③ under the condition of ②, when CE = 4, calculate the area of quadrilateral abdc

① Prove: as shown in the figure, in the circle ∠ ACB = ∠ BDA = 60 °, and ∵ AE and be are the bisectors of ∠ BAC and ∵ ABC, ∵ BAC = 120 °, and ∵ be = 12 (∵ ABC, ∵ BAC) = 60 °, and ∵ BDE is an equilateral triangle

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