Is there an automated way to set type to display around a circle in InDesign, like the below image?
If you have access to it, this can be done much easier in Illustrator with the Rotate tool and the Transform Again
Command + D action. First set up a center point with guides:
Next, type the first line of text and align it to the horizontal guide:
Select the rotate tool and set the cross-hair to the intersect of the guide set up in step one:
Option + Click & Drag text to desired spacing around center axis:
Command + D , repeat until circle is completed:
Hope this helps!
As already mentioned, this would be much easier to do in Illustrator. I'll show you another method which may be more beneficial and easier to maintain.
Draw a circle and give it no fill or stroke. We don't actually want to see the circle; we're using it as a guide for our transforms, nothing more (you can temporarily give it a stroke so that it's easier to work with if you want).
Create a single instance your type inside the circle and group them.
With the group selected, go to Effect → Distort & Transform → Transform... Set an appropriate rotation angle and a number of copies; you can ignore everything else.
You can now change your text, update its positioning etc. and all the rotated copies will automatically update too.
You can create sections with different type by duplicating and rotating the group, each group has a single text object and single transform effect instance that you can easily update.
You can then copy and paste the result in to InDesign, or more likely save and place the Illustrator document in InDesign to easily update it.