Math Circle Problem

Solution
Is AC a straight line? If so:

Angle ACD is 55* (subtends the same arc as angle ABD)

Therefore, angle BDC 33* (angle sum of triangle CDE)

Then you can find DE using the sine rule.
DE/sin55* = 4/sin33*
DE = 4sin55*/sin33*
DE = 6 (approx.)

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