Elegance is the key - Part II

Geometry Level 3

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

This is an original problem.
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