Inscribed and Circumscribed Circles

Geometry Level 2

\(ABCD\) is a square. \(\Gamma_1\) is a circle that circumscribes \(ABCD\) (i.e. \(\Gamma_1\) passes through points \(A, B, C\) and \(D\)). \(\Gamma_2\) is a circle that is inscribed in \(ABCD\) (i.e. \(\Gamma_2\) is tangential to sides \(AB, BC, CD\) and \(DA\)). If the area of \(\Gamma_1\) is \( 100\), what is the area of \(\Gamma_2\)?

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