Ptolemy's Riddle III

Geometry Level 2

A cyclic quadrilateral \(ABCD\) is constructed within a circle such that \(AB = 3, BC = 6,\) and \(\triangle ACD\) is equilateral, as shown below:

If \(E\) is the intersection point of both diagonals of \(ABCD\), what is the length of \(ED,\) the blue line segment in the diagram?

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