# Two similar equilateral triangles in a circle

Geometry Level 5

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

If $$E$$ is the midpoint of the side $$BC$$ of the larger orange triangle which has a side length of $$16$$ and side $$DE$$ of the smaller triangle is parallel to $$AC$$, find the length of $$DE$$ correct to 2 decimal places.

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