Why window DHCP server is connected to a cisco routing switch in a LAN

We have Cisco WS-C3560X-48P-L switch within our LAN, which connects to a modem and through the fibre network to the service provider. This switch does the internet routing  for our network.

We have PDC Windows 2008 server , which is also our DHCP server.
I have observed that the LAN port of the DHCP server is connected to one of the port in the Cisco 3560 switch.

We have another Cisco Core switch and on this switch all the remaining servers LAN ports get connected and also the uplinks from other segment comes and  gets connected to this switch.

So there is also a RJ45 cable patched between the Core and the Cisco 3560.

I am not clear as  why the DHCP LAN port is patched into the Cisco 3650 rather than the Core switch.
We have been allocated 10.14.116/22 to our network and the scope 10.14.116.1 - 10.14.119.254  is configured on our DHCP server.

I am not able to understand this connectivity. Please tell me technical how it works.
Any tutorial or link to understand this type of infrastructure connectivity will be great.

I am not clear as  why the DHCP LAN port is patched into the Cisco 3650 rather than the Core switch. <-- I think no one here can answer this ^^

For technically why it works, you provided information is not enough to understand, and many scenario can do. Most common case is the core switch has configured ip helper to relay the DHCP request to your server

The port/server can be connected anywhere i.e in any switch as long as the particular port is under the same relevant vlan. Which physical switch, it does not matter. But since you have to connect it somewhere so anywhere, keeping the port config same.......

It all depends on what is connected to the core WS-C3560X-48P-S switch.  IP helpers can be setup that route all DHCP broadcasts to the known DHCP server.