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I have 2 polygons that represent districts from neighboring cites. The Polygons extend 1.5 miles out from the city border. There is an area between the 2 cities where these polygons overlap each other.

Is there a tool that i can input the 2 polygons and have it output them with the borders meeting in the middle between the two cities instead of overlapping?

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You could try running "euclidean allocation" tool link on the original city border polygons, setting the "maximum distance" parameter to 1.5 miles. Vectorize the results if necessary.

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The union tool would separate each region (though not in the middle), under the geoprocessing tab. select your two polygons and union will create 3 polygons; 1 for each separate city and a third for the overlapping region.

Otherwise, you could edit each polygon using the editor toolbar to redraw their borders.

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