Earth-boring tools may have a body, a cutting element attached to the body at a first location, and a formation-engaging structure attached to the body at a second location. The formation-engaging structure may be movable during a drilling operation between a first position and a second position. In the first position, the formation-engaging structure may be located rotationally behind the cutting element at a first radial distance from a longitudinal axis of the body at which the cutting element will at least initially shield the formation-engaging structure from engaging a formation. In the second position, the formation-engaging structure may be located at a different second radial distance from the longitudinal axis of the body at which the formation-engaging structure will engage a formation.