# 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 $$b$$.

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