A tool that calculates distance statistics (such as min, max, average) from a given point to the vertices of a polygon.
Couldn't you use something like Feature Vertices To Points—Data Management toolbox | ArcGIS Desktop and then use Generate Near Table—Help | ArcGIS Desktop to calculate proximity from your given point to each vertex.
Summary Statistics—Help | ArcGIS Desktop on the near table will give you what you want.
This will be a better way to accomplish what you want today rather than request an overly specific tool...
I have already tried the method you are proposing and it has worked. I just thought it might be useful to have a tool that implements it directly. Thank you!
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