Notes
diagonal in a square solution

Diagonal in a Square

Solution by Equilateral Triangles

In the diagram above, $E$ is on the diagonal so that $A E$ is the same length as $F C$, namely $a$. The length of $E F$ is then $c - a$ which, from the statement of the problem, is $b$. By symmetry, $B E$ is also of length $b$ so $B E F$ is an equilateral triangle and angle $A \hat{F} B$ is $60^\circ$.