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I have some polygon layers (parcels) that have vertexes drawn around curves, as if traced. How do I click and drag to draw vertexes in a smooth shape? Big difference between what was originally there, and what I drew in. Hopefully this helps illustrate what I am wanting to accomplish.

enter image description here

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    What format are you storing your data in? It is important to note that shapefiles cannot store true curves/arcs. You must use a geodatabase if you want three point (start radius end) arcs. Otherwise, even if you use the Arc tool, it will be converted to segments upon sketch completion. – Chris W Nov 3 '14 at 22:31
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If you want to draw features like the one you posted you should use the Arc tool. It is available on the Editing toolbar from the dropdown menu which usually displays Trace. There are a couple of different Arc functions, check them out here.

You can also make Bezier curves, which are easier to reshape.

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There's also a downloadable tool called Curves and Lines, originally developed for preparing data for the parcel fabric, that might do what you want. Takes some time to figure out what tolerances to set the parametes to, so try it on a copy of your data first. This is designed to clean up existing features, not add new ones.

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This tool should do what you are asking for Smooth Line (Cartography) without having to click and drag.

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