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I have encountered the following problem: I have a set of lines in ArcMap. I need to place points at specified (not regular) distances along these lines. The distances are not the same between lines.

I feel its a waste of time to manually measure each distance and Place a Point there.

Any tips for a quicker way?

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I'd suggest looking into the linear referencing tools. This lets you define your lines as routes and create tables that will place events along these routes at specified measurements.

You should be able to make tables with the measurements you need to place points at, then create an event layer along your route with the points. These can then be exported to a separate featureclass if needed.

These articles should get you started:

Creating routes from lines - http://desktop.arcgis.com/en/arcmap/10.3/guide-books/linear-referencing/using-existing-linear-features-to-create-routes.htm

Create event table - http://desktop.arcgis.com/en/arcmap/10.3/guide-books/linear-referencing/about-creating-event-tables-in-arccatalog.htm

Display Events on route - http://desktop.arcgis.com/en/arcmap/10.3/guide-books/linear-referencing/adding-route-events-using-the-linear-referencing-toolbox.htm

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