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A graph \( G \) with \( k \) vertices is distance magic if the vertices can be labeled with numbers \( 1, 2, \ldots, k \) so that the sum of labels of the neighbors of each vertex is equal to the same constant \( \mu_0 \). We present a construction of distance magic graphs arising from arbitrary regular graphs based on an application of magic rectangles. We also solve a problem posed by Shafig, Ali, and Simanjuntak.