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This dot that appears at anchor points and you can drag to curve / arc the corner. This tool is useful but I want to know how to make it happen in the corners where it doesn't automatically appear?

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    The correct answer is that artwork must be larger than pixel-level to use Live Corners. Hopefully the question will be opened and answered correctly. – Andrew Swift May 10 '18 at 18:06
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This is called "Live Corners". This is a new feature to easily edit one or multiple corners at once.

A common reason why the corner widget might disappear is that your artwork is too small.

Working at sizes smaller than a single pixel can make live corners unavailable.

You can learn about Live Corners and see videos about it on Adobe's page: Live Corners

Here is the explanation from the related help document, Live Corners From the Adobe Help Document:

You can select one or more corner anchor points in a simple path, or multiple anchor points across several paths in your artwork. When selected, a Live Corners widget appears next to each corner point. Dragging a widget causes the corner point to change shape, into one of three available corner types. The three available corner types are Round, Inverted Round, and Chamfer.

The Live Corners widget (When it appears)

The Live Corners widget is enabled when:

  • you select the Direct Selection tool (white arrow)
  • you have a path selection containing corner points
  • the artwork is sufficiently large (corner radii bigger than 1 pixel)

A Live Corners widget is displayed next to a corner when you select:

  • One or more path(s) that have corners.
  • One or more rounded corners

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