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I am using ArcMap 10.1 and I would like to know if there is a way to draw circles at a specific distance from a georeferenced coordinate. I have a property and I would like to know how far you can walk from it within different amounts of time, and I would like to portray this with multiple circles.

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Basically, this is just Buffer. Since you want to make multiple buffers at once, though, the Multiple Ring Buffer tool would be more appropriate.
Multi ring buffer
and the default will be the crs/gcs of the input unless you change it with the unit option.

It's worth considering that plain distance is not walking distance. Walking routes are restricted: a person can't (reasonably) walk over a building, an interstate highway, a river/stream, etc., and it's harder to walk up a steep hill than along a level path. A more accurate analysis would use Cost Distance tools, which are basically Euclidean Distance plus additional considerations -- but you'd need additional data (land cover, or slope, etc.).

Buffers will give you a very reasonable approximation, however!

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Also see This Answer for a Arc tool that can make buffers given a range and interval -- easier than Multiple Ring Buffer for a large enough number of buffers! – Erica Aug 15 '14 at 15:11

Using the Buffer tool, with different buffer distances, will yield circles around your point.

If you want accurate walking time polygons, and have a Network Analyst license, look into Service Area Analysis

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