In this paper, reverse Bonnesen style inequalities are discussed. Namely, given a convex domain \(K\) in the Euclidean plane \(E^2\), let \(P\), \(A\), \(r_I\), \(r_E\), \(d\) stand for the perimeter, the area, the in-radius, the circum-radius and the diameter of \(K\) respectively. Then the following inequalities hold true for the isoperimetric deficit \(\Delta_2(K) = P^2-4\pi A\) of \(K\): \[ \Delta_2(K) \leq 2\pi P\left(r_E-r_I\right), \quad \Delta_2(K) \leq 2\pi P\left(\frac{d}{2}-r_I\right), \]
\[ \Delta_2(K) \leq \frac{\pi P^2}{A}\left(r_E^2-r_I^2\right),\quad \Delta_2(K) \leq 4\pi^2\left(r_E^2-r_I^2\right), \]
\[ \Delta_2(K) \leq \frac{\pi P^2}{A}\left(\frac{d^2}{4}-r_I^2\right),\quad \Delta_2(K) \leq 4\pi^2\left(\frac{d^2}{4}-r_I^2\right). \] Moreover, the equalities hold true if and only if \(K\) is a disc.