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I have two layers. One contains points (lat/lng) and the other contains lakes (polygons). I want to generate a table that shows, for every point, the distance to every lake.

What tool in the toolbox is designed for this task?

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This sounds like the use case for the Generate Near Table tool which:

Calculates distances and other proximity information between features in one or more feature class or layer. Unlike the Near tool, which modifies the input, Generate Near Table writes results to a new stand-alone table and supports finding more than one near feature.

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