I was going to suggest the "mathematical approach", but when I finished coding it, saw that roboticus had "beat me to the punch".  So, at least one other person interpreted your question the same way that I did :-)

Here's my solution:

#!/usr/bin/perl -w

# Strict
use strict;
use warnings;
use Data::Dumper;

# User defined
my $text = "
                                       It's
                                    been said
                                  ever so often
                                by many an expert
                              that in ol' plain text
                                one neer can get a
                                 round tuit, but
                                    just look
                                       here
";

# Main program

$text =~ s/(?<!\s) (?!\s)/@/gms;             # Turn inner spaces into 
+'@'
print "Debug1>  text = [$text]\n";           # Show text
$text =~ s/\s+//;                            # Strip all other spaces
$text =~ s/\n/@/gs;                          # Convert newlines to '@'
my @text = grep { /\S/ms } split //, $text;  # Split text into charact
+ers

# Find the mass of the diamond
my $mass = (my $temp = $text) =~ s/\S/./g;
print "Debug2> mass = [$mass]\n";

# Circle mass 'm' = pi * r^2, so the radius 'r' = sqrt(m / pi)
my $radius = sqrt($mass / 3.14159265358);
print "Debug3> radius = $radius\n";

# Format the text into a circle, 
my $circle = "";
my $aspect = 1.0;
for (my $row = -($radius + 10); $row <= ($radius + 10); $row++) {
    for (my $col = -($radius + 10); $col <= ($radius + 10); $col++) {
        my $char = " ";
        if (($aspect * $row) ** 2 + $col ** 2 <= $aspect * ($radius **
+ 2)) {
            $char = shift @text || '*';
        }
        $circle .= ($char eq '@'? ' ': $char);
    }
    $circle .= "\n";
}

# Show the resulting circle
print "$circle\n";

__END__

Output:
Debug1>  text = [
                                       It's
                                    been@said
                                  ever@so@often
                                by@many@an@expert
                              that@in@ol'@plain@text
                                one@neer@can@get@a
                                 round@tuit,@but
                                    just@look
                                       here
]
Debug2> mass = [120]
Debug3> radius = 6.18038723238067


             It's be
            en said e
           ver so ofte
           n by many a
           n expert tha
           t in ol' pla
           in text one
           neer can get
            a round tu
            it, but ju
             st look
               here
[download]

What the above solution boils down to is this:  count up the number of characters in the original text, excluding spaces which are outside of the "block" of text.  Calculate the "mass" (which in your case is 120), and then use it to find the characters which are within the circle.

You can test the veracity of this solution by changing the text.

For example, if you choose $text to be:

my $text = "
  This document is intended to give you a quick overview of the Perl
  programming language, along with pointers to further documentation.
  It is intended as a \"bootstrap\" guide for those who are new to the
  language, and provides just enough information for you to be able to
  read other peoples' Perl and understand roughly what it's doing, or
  write your own simple scripts.

  This introductory document does not aim to be complete. It does not
  even aim to be entirely accurate. In some cases perfection has been
  sacrificed in the goal of getting the general idea across. You are
  *strongly* advised to follow this introduction with more information
  from the full Perl manual, the table of contents to which can be
  found in perltoc.
";
[download]

then you'll get a nice, circular output of:

                    This docume
                  nt is intended
                 to give you a quic
               k overview of the Per
              l programming language,
               along with pointers to
             further documentation. It
            is intended as a "bootstrap
            " guide for those who are ne
           w to the language, and provid
           es just enough information fo
           r you to be able to read other
            peoples' Perl and understand
           roughly what it's doing, or wr
           ite your own simple scripts.
           This introductory document doe
           s not aim to be complete. It d
           oes not even aim to be entirel
           y accurate. In some cases per
           fection has been sacrificed i
            n the goal of getting the ge
            neral idea across. You are
             *strongly* advised to foll
             ow this introduction with
               more information from
               the full Perl manual,
                 the table of conte
                 nts to which can
                   be found in p
                      erltoc.
[download]

You can vary $aspect to change the aspect ratio of the circle as well.  For example, with $aspect = 1.7, the last example looks even more "circular":

                   This docume
               nt is intended to g
             ive you a quick overview
            of the Perl programming lan
         guage, along with pointers to f
        urther documentation. It is intend
       ed as a "bootstrap" guide for those
       who are new to the language, and pro
      vides just enough information for you
     to be able to read other peoples' Perl
     and understand roughly what it's doing,
      or write your own simple scripts.  This
      introductory document does not aim to b
     e complete. It does not even aim to be
     entirely accurate. In some cases perfec
      tion has been sacrificed in the goal
       of getting the general idea across.
       You are *strongly* advised to follo
         w this introduction with more in
          formation from the full Perl
            manual, the table of conte
              nts to which can be fo
                 und in perltoc.
[download]