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I need a circle symbol that is somehow compatible (from a layout point of view) with square and triangle. As you can see in the following example

documentclassarticle
usepackageamsmath
usepackageamsthm
usepackageamsfonts
begindocument
$circ AB$, $bigcirc AB$, $square ABCD$, $triangle ABC$, 
enddocument

the square and the triangle are a perfect match, but none of the circle symbols match. Is there a way to get a circle aligned with bottom line of the text and with a comparable height as the other two symbols? In maths mode.

I've seen this question, but is not the right one for my situation:
Is there a circle symbol?

You can scale bigcirc down:

documentclassarticle
usepackageamsmath
usepackageamsthm
usepackageamssymb
usepackagegraphicx

makeatletter
DeclareRobustCommandiscirclemathordmathpaletteis@circlerelax
newcommandis@circle[2]%
 begingroup
 sboxz@raiseboxdepth$m@th#1bigcirc$%
 sboxtw@$#1square$%
 resizebox!httw@useboxz@%
 endgroup

makeatother

begindocument

$iscircle AB$, $square ABCD$, $triangle ABC$,

enddocument

Some other possibilities: use ocircle from wasysym, raised slightly (the regular symbol is rendered below the baseline), or use TikZ and print a tight circle around a lower case letter (but don't print the letter).

The commands can be defined in a simple way that scales with the font but not with sub- and superscript, or as a more math-aware version using mathchoice. The solution in the other answer is also included, note that the circle is a little flat in the subscript of the normal size example, but round in the Huge version.

documentclassarticle
usepackageamsmath
usepackageamsthm
usepackageamsfonts
usepackagewasysym
usepackagetikz
makeatletter
DeclareRobustCommandiscirclemathordmathpaletteis@circlerelax
newcommandis@circle[2]%
 begingroup
 sboxz@raiseboxdepth$m@th#1bigcirc$%
 sboxtw@$#1square$%
 resizebox!httw@useboxz@%
 endgroup

makeatother
newcommandwacircsimpleraisebox0.2ex$ocircle$
newcommandtkzcircsimpletikznode[circle,inner sep=0,outer sep=0,draw]$phantomo$
newcommandwacircscalemathchoice%
raisebox0.2ex$displaystyleocircle$%
raisebox0.2ex$textstyleocircle$%
raisebox0.2ex$scriptstyleocircle$%
raisebox0.2ex$scriptscriptstyleocircle$%

newcommandtkzcircscalemathchoice%
tikznode[circle,inner sep=0,outer sep=0,draw]$displaystyle phantomo$%
tikznode[circle,inner sep=0,outer sep=0,draw]$textstyle phantomo$%
tikznode[circle,inner sep=0,outer sep=0,draw]$scriptstyle phantomo$%
tikznode[circle,inner sep=0,outer sep=0,draw]$scriptscriptstyle phantomo$%


begindocument
$squareiscircle BA_iscircle AB_iscircle AB$

$squarewacircsimple BA_wacircsimple AB_wacircsimple AB$

$squarewacircscale BA_wacircscale AB_wacircscale AB$

$squaretkzcircsimple BA_tkzcircsimple AB_tkzcircsimple AB$

$squaretkzcircscale BA_tkzcircscale AB_tkzcircscale AB$

Huge
$squareiscircle BA_iscircle AB_iscircle AB$

$squarewacircsimple BA_wacircsimple AB_wacircsimple AB$

$squarewacircscale BA_wacircscale AB_wacircscale AB$

$squaretkzcircsimple BA_tkzcircsimple AB_tkzcircsimple AB$

$squaretkzcircscale BA_tkzcircscale AB_tkzcircscale AB$
enddocument

In my opinion the TikZ version looks better in the normal font (considering line width) but in the Huge version the wasysym symbol looks better.