How to convert one shape into another?

Roger,

As I (mis)understand it, it is quite easy to obtain the desired creation and positioning of the inscribed regular polygons and stars.

You can, Smart Guides/double Aligning being your friends:

1) Create the circle;

2) Create a regular polygon or star with a radius equalling half the W(idth)/H(eight) of the circle;

3A) For any regular polygon or star ClickDrag the polygon/star choose the Anchor Point of an (outer) point that corresponds to one of the 4 Anchor Points of the circle, and ClickDrag the polygon/star by that to snap to the corresponding Anchor Point of the circle;

3B) As an alternative for a regular polygon or star with an even number of (outer) points, Select both the regular polygon/star and the circle, then use Center Align both vertically and horizontally with the circle as key object.

The image below shows the outcome for a hexagon, a pentagon and a star with 5 points; the hexagon was made with 3B) but could just as well have been made with 3A using either side Anchor Point of the circle; the pentagon was made with 3A) using the top Anchor Point of the circle; the star with 5 points was made with 3A) using the bottom Anchor Point of the circle; in all cases Round Joins are used to avoid Miter Joins sticking out so the exact fits are obvious.

That conversion feature in InDesign is dangerous.

https://youtu.be/wGxyYdkjfOQ 

Are you talking about something like this?

Or something like this?

Or something else?

I just drew a Triangle by clicking on the "center" of the circle and drawing outward, with the Smart Guides active, it eventually intersects with the circle and that gives me all the precision needed BUT it should be a simple "one-click" command somewhere,,, Think of my poor students learning Illustrator for the first time...