<p>We present a rigorous global optimization-based approach to a problem arising in discrete geometry: covering a rectangle with six identical circles while minimizing their radius. Our main contribution lies in formulating and solving this problem using mathematical programming combined with exact global optimization relying on interval-based computation. This approach not only enables the numerical proof of a theoretical result, but also certifies the accuracy of computed values by enclosing them within verified bounds, thus certifying decimal digits. This brings a strong evidence of the role of mathematical programming and rigorous exact global optimization in addressing geometric covering problems with provable precision.</p>