The Unit Square in the Unit Circle

Geometry Level 5

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 \(100a+10b+c\).

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