Router A does not have interfaces configured for eigrp and is connected to core-router, router C is connected to core-router and interfaces are configured for eigrp. How do router c knows about router A??? Note that core-router does not have "redistribute connected" configured, thanks to all in advanced.
In such cases, you need to redistribute routes into EIGRP. If you just do 'redistribute connected' it will only redistrute the network for the link between A and the core router. If you have other networks connected to router A, you need to either run a routing protocol between A and the core-router OR create a bunch of static routes on the core router and redistribute them into EIGRP.
Paresh, my question was only "how come router C knows about router A if router A does not have EIGRP interfaces configured? in other words the rest of the network behind router C knows about A even thou router A is not supposed to be participating in EIGRP?
Router C will come to know about the routes on router A, only if Core router has some static routes configured for Router A's subnet and they are reditsributed on core router.
But this will not make Router A to communicate with the router C untill and unless the Router C's subnets/networks are there in router A's routing table.This can be done either configruing static routes on Router A for the Router c's subnet or pointing a default router on Router A with the next-hop ip of core router.