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Two circles are circumscribed and inscribed about a square ABCD of side 2 units. If P and Q are two points on respective circles, ∑(PA)2 - ∑(QA)2  = ...........

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Let centre of square (point of intersection of diagonals) be origin. 

Vertices of square are A(1, 1), B(–1, 1), C(–1, –1) and D(1, –1). Radius of circumscribed or inscribed circles are 2 and 1, respectively.

Let any point P and Q on circumscribed and inscribed circles, respectively, be (√2 cosα,√2 sin α) and (cosβ, sinβ). Therefore,

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