For the convenience of description, set a dot as shown in the figure and connect AC to point O.

①△AEO is similar to △CBO (the two angles are equal), AE/EO=BC/BO. According to the meaning of the question, BE=EO+OB=4, AE=3, BC=5, EO= 1.5, BO=2.5.

② According to Pythagorean theorem, in the right angle △AEO, AO 2 = AE 2+EO 2, then AO= 1.5*√5, and in the same way, CO=2.5*√5 can be obtained.

③ AC=AO+CO=4√5。

④ According to Pythagorean Theorem, in right angle △ACD, DC 2 = AC 2-AD 2, then DC=√7 1≈8.426.