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I have a polygon shapefile which represents a study area (island). I also have a point shapefile representing some villages. What I am after is to locate for each village point the nearest point along the shoreline (the latter being represented by the edge of the polygon shapefile). Is there any tool to accomplish this in arcGIS 10.1 (advanced license)?

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First you have to convert your polygon to lines. Then you can use Generate Near table. With this tool you can create table with few parameters (coordinates, angles) of nearest objects to your input objects. You can get this coordinates and create point layer if you need to visualise that.

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