# Diagonal in a Square +-- {.image} [[DiagonalinaSquare.png:pic]] > The point lies on the diagonal of the square so that $a + b = c$. What's the angle? =-- ## Solution by [[Equilateral Triangles]] +-- {.image} [[DiagonalinaSquareLabelled.png:pic]] =-- 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 $60^\circ$.