\(ABCD\) is a trapezoid 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 \(\Gamma\)?
