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.

\sqrt{ab}

\sqrt{(a+b)a}

\sqrt{(a-b)b}

\sqrt{(a+b)b}

(a^{2} - b^{2})