I would like to add that there is a firewall at gw.mydomain.tld and it has in its firewall script (ip_chains) assigned two IP ranges for public and private. public IPs. xxx.yyy.56.zzz and private IPs are xxx.yyy.39.zzz
And the machine that I am using as a dhcp server is in the 39 range which will further broadcast dhcp to its subnet. Just to make it clear.