Circle Inscribed in a Trapezium

Geometry Level 3

\(ABCD\) is a trapezium with \(AB < CD\) and \(AB\) parallel to \(CD\). \(\Gamma\) is a circle inscribed in \(ABCD\), such that \(\Gamma\) is tangent to all four sides. If \(AD = BC = 25 \) and the area of \(ABCD\) is \( 600\), what is the radius of \(\Gamma\)?

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