# Playing with squares and circles

Calculus Level 5

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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