The Unit Square in the Unit Circle

Cyclic quadrilateral $ABCD$ is circumscribed by a unit circle. Let $E,F$ be the orthocenters of $\triangle BCD, \triangle ACD$ respectively. If $ABEF$ is a unit square, then the value of $[ABCD]$ can be expressed as $\dfrac{\sqrt{a}}{b}+c$ with positive integers $a,b,c$ and $a$ square-free.

Find $100a+10b+c$ .