Using the properties of isosceles triangle; Pythagorean theorem; The median line theorem in triangle,

Solution: extend the extension line from AF to BC to g point,

AE = BE，

∴∠ABE=∠BAE，

∵AF⊥AB，

∴∠ABE+∠AGB=90，∠BAE+∠EAG=90，

∴∠AGB=∠EAG，

∴AE=EG，

∴E is the midpoint of BG

∴ It is easy to find EF= 12AB=3, FG=AF=4, and △EFG is a right triangle.

∴EG=5，

∴CE=EG-CG=EG-AD=5-2.7=2.3.

So the answer is: 2.3.