The topic is wrong. As shown in the triangle DBC, CD=DB=2 and the angle CDB=30 degrees. As the vertical DB of CE, CE= 1 is obtained.

DE=√3, BE=2-√3, BC squared =8-4√3, BC is about 1.0352, extending BD to A makes BA=2BC about 2.074,

Triangle ABC meets the requirements of the topic, but the angle A is less than 30 degrees, and the original conclusion is wrong.