The design and study of structures exhibiting bound states in the continuum (BICs) are the object of continuous works in wave physics. These long-lived states which are localized in some parts of the system without interacting with the background have found several potential applications due to their high sensitivities to weak perturbations, in particular in filtering and sensing. In this paper, we present a theoretical demonstration of BICs in an asymmetric loop composed of two arms of lengths d1 and d2 with both an experimental validation in the radio-frequency (RF) domain using coaxial cables and a numerical validation in the infrared (IR) domain using plasmonic metal-insulator-metal nanometric waveguides. The analytical study is performed by means of the Green’s function method, whereas the numerical calculation is obtained using finite element method. The BICs correspond to localized resonances of infinite lifetime inside the loop, without any leakage into the surrounding waveguides. We demonstrate that the condition for the existence of the BICs is to make the lengths of the two arms (d1 and d2) commensurate with each other. At the corresponding frequencies, one of the two degenerate modes of the isolated loop (associated with the clockwise and anti-clockwise propagations) couples to the waveguides while the other remains unaffected. When the lengths are slightly shifted from the BICs, the latter transform to Fano resonances exhibiting dips in the transmission spectra and sharp peaks in the density of states (DOS). As an application of our design, we show the efficiency of the Fano resonances in designing an efficient gaz-sensor with a high sensitivity and factor of merit in the IR domain. In addition, we derive an exact formula about the proportionality between DOS and the derivative of the argument of the determinant of the scattering matrix (Friedel phase) for a lossless structure; then, we discuss the validity and deviation from this rule when the loss is increased.