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Is it possible to label the "edge" of a point symbol in ArcMap when using leader lines? I would like to offset the leader so the line does not overlap the point symbology. In the past I have converted my points to polygons to leverage anchors, but want to know if there is another cartographic method to addressing this issue. If have included a picture displaying the overlap I want to remove.

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You can adjust the offset to the change the position of the line leader. For example, here is the default position of the line leader:

enter image description here

After changing the offset, it becomes like this:

enter image description here

To adjust the offset of the line leader, you can use the following steps:

Go to Layer Properties -> Labels -> select Symbol -> Edit Symbol -> Advanced Text -> Text Background (Properties) -> Type (Simple Line Callout) -> Symbol

enter image description here

-> Edit Symbol -> Cartographic Line Symbol -> Line Properties -> Offset

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In the above example, I used an offset of 7.000, but you can change the position based on the desired location. The offset is only in one direction, There is no option to adjust the X-Offset and Y-Offset.

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