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I want to reduce the number of Vertices of a circle but I cannot find out the input box for setting this. I am now at the Edit Mode and already selected a circle. Where is the input box?

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Steps

  1. Press Shift + A and select Circle to add a new circle to the scene.

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  2. After clicking the Circle, the input box of Vertices is now shown in the left hand side menu.

    enter image description here


Explanation

The editbox for that only appears directly and automatically after you added the circle to the scene. If you switch to editmode after that then you can't change it anymore that way.

You'll need to undo the adding, add it again and change the value right away and THEN go into editmode to work on it further.

Alternatively you can just stay in editmode, remove all vertices and add a new circle, it'd be the same in the end.

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As an adiition to already given answer, this is normal behaviour which means that any operator settings won't be accessible as soon as you leave the settings panel (i.e. execute any other operator).

Method without Recreating Circle

Although in your case it's possible not to delete anything rather than just dissolve unneeded vertices (depending on the result you're aiming to it might be not worth efforts for primitives, although sometimes geometry shouldn't be deleted in these cases).
For easing selection step use Select > Checker Deselect (make any vertex active and select all first).

screenshot of dissolving checker deselected verts

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