letting apart the humor (which incidentally make your post harder to understand for non native english speakers.. :), you never set $resize background to white! I didnt follow all your geometry calculus, but be aware the the default background for a GD image is black:

perl -MGD -e"$im = new GD::Image(100,100);open $fh,'>','out.jpg';binmo
+de $f; print $fh $im->jpeg"
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The above print a nice black image.

Simplfying the whole I think you can start from something like the following code, which does what you are looking for

use strict;
use warnings;

use GD;
GD::Image->trueColor(1);

# gray image 100x100
my $im_gray = new GD::Image(100,100);
my $gray = $im_gray->colorAllocate(127,127,127);
$im_gray->filledRectangle(0, 0, 100,100, $gray);
open my $fh_gray,'>','gray.jpg';
binmode $fh_gray; 
print $fh_gray $im_gray->jpeg;


# red image 100x100
my $im_red = new GD::Image(100,100);
my $red = $im_red->colorAllocate(255,0,0);
my $black = $im_red->colorAllocate(0,0,0);
$im_red->filledRectangle(0, 0, 100,100, $red);
# with a black circle
$im_red->ellipse(50,50,100,100,$black);
open my $fh_red,'>','red.jpg';
binmode $fh_red; 
print $fh_red $im_red->jpeg;


# copy resized red image scaled 50% and centered inside the gray one
$im_gray->copyResized($im_red,25,25,0,0,50,50,100,100);

open my $fh_both,'>','both.jpg';
binmode $fh_both; 
print $fh_both $im_gray->jpeg;
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L*