F3 Geometry

[ajax3245]

The letter E is ，not F.

 

[Freeman]

Let O be the mid-point of AC, OE intersects BC at D'. O is the circumcenter of A,C,E.
∠COE=2∠CAE=∠CAB, △COD'~△CAB. D' is the mid-point of BC, D'=D.
DE=OE-OD=OC-AB/2=(AC-AB)/2.