Most impacts occur at an angle with respect to the horizontal plane. This is primarily reflected in the ejecta distribution, but at very low angle structural asymmetries such as elongation of the crater and nonradial development of the central peak become apparent. Unfortunately, impact craters with pristine ejecta layers are rare on Earth and also in areas with strong past or ongoing surface erosion on other planetary bodies, and the structural analysis of central peaks requires good exposures or even on-site access to outcrop. However, target properties are known to greatly influence the shape of the crater, especially the relatively common target configuration of a weaker layer covering a more rigid basement. One such effect is the formation of concentric craters, i.e., a nested, deeper, inner crater surrounded by a shallow, outer crater. Here, we show that with decreasing impact angle there is a downrange shift of the outer crater with respect to the nested crater. We use a combination of (1) field observation and published 3-D numerical simulation of one of the best examples of a terrestrial, concentric impact crater formed in a layered target with preserved ejecta layer: the Lockne crater, Sweden; (2) remote sensing data for three pristine, concentric impact craters on Mars with preserved ejecta layers further constraining the direction of impact; as well as (3) laboratory impact experiments, to develop the offset in crater concentricity into a complementary method to determine the direction of impact for layered-target craters with poorly preserved ejecta layers.