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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