Playing with squares and circles

Calculus Level 5

direction of velocity of square is as shown

direction of velocity of square is as shown

A circle of unit radius is placed at origin as shown. A square of unit side length moves with constant velocity of \(2\) units in the direction as shown. When \(OC=\dfrac{1}{4}\), if the rate of change of shaded area can be represented as \(\dfrac{\sqrt{A . B}}{C}\) where \(\color{blueviolet}{A<B}\), then find the rate of change of shaded area when \(OC=\dfrac{1}{A}\). If your answer is of the form \(\dfrac{X\sqrt{Y}}{Z}\) where Y is square free and \(X\) and \(Z\) are co-prime to each other, then enter the value of

\(X . Y . Z\).

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