Try this (some slight changes to see a better circle)

#!/usr/bin/perl

use strict;
use warnings;
use List::Util qw( max min );

my $max = 40;

my @aoa = map { [ ( 'o' ) x ($max + 1) ] } 0..$max  ;

display( @aoa );

# @to_change will contain [y1,x1],[y2,x2]...
#my @to_change = illuminate( 5, 4, 6 );
my @to_change = illuminate( $max >> 1, $max >> 1, $max - 2 >> 1 );

print "\n";
$aoa[$_->[0]][$_->[1]] = 'x' for @to_change;
display( @aoa );

sub illuminate
  {
  my @to_change;
  my $center_r = shift;
  my $center_c = shift;
  my $radius     = shift;
  #...
  for my $row ( 0 .. $#aoa )
    {
    my $delta_x = eval { int sqrt $radius ** 2 - ($center_r - $row) **
+ 2 };
    if( defined $delta_x )
      {
      my $low = max 0, $center_c - $delta_x;
      my $high = min $#{ $aoa[$row] }, $center_c + $delta_x;
      push @to_change, map [ $row, $_ ], $low .. $high;
      }
    }
  return @to_change;
  }

sub display
  {
  foreach my $row ( @_ )
    {
    foreach my $col ( @$row )
      {
      print $col;
      }
    print "\n"
    }
  }
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