Two similar equilateral triangles in a circle

Geometry Level 4

Two equilateral triangles reside in a circle, one on top of the other as shown in the figure above.

If EE is the midpoint of the side BCBC of the larger orange triangle which has a side length of 1616 and side DEDE of the smaller triangle is parallel to ACAC, find the length of DEDE correct to 2 decimal places.

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