We study the epsilon-level sets of the signed distance function to a planar Jordan curve Gamma, and ask what properties of Gamma ensure that the epsilon-level setsare Jordan curves, or uniform quasicircles, or uniform chord-arc curves for all sufficiently small epsilon.Sufficient conditions are given in term of a scaled invariant parameter for measuring the local deviation of subarcs from their chords. The chordal conditions given are sharp.
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