In the present paper, we prove lower and upper bounds for each of the ratios \(GA/\delta\), \(GA/\overline{d}\) and \(\Delta\), in terms of the order \(n\), over the class of connected graphs on \(n\) vertices, where \(GA\), \(\delta\), \(\overline{d}\) and \(\Delta\) denote the geometric-arithmetic index and the minimum, the average and the maximum degrees, respectively. We also characterize the extremal graphs corresponding to each of those bounds. We also prove bounds where, in addition to the geometric-arithmetic index \(GA\), the Randić index \(Ra\) and the maximum degree \(\Delta\) are involved.