Elegance is the key - Part II

Geometry Level 3

In the above figure, points (E,D,F) (E,D,F ) and (B,A,F) (B,A,F) are collinear, and EC=CD=BC \overline{EC} = \overline{CD} = \overline{BC} . Also, CBBA CB \bot BA . The length of ED ED is a a , and the length of DF DF is b b . Then find the length of FB FB in terms of aa and bb.

This is an original problem.
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