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Locking linear elements to reference planes is pretty simple, I normally use the align tool and after the element is aligned I check the lock icon to lock the element to the plane. But if what we want to lock to a plane is a circle, it is not so straight forward. The trick to do it, is to unhide the circle center mark.
To do that, you need to select the circle, and go to the properties tab and check the Center Mark Visible checkbox to unhide the center mark. After you've done that you will see a cross at the center of the circle that will allaow you to lock the center to one or two reference planes.