I'm guessing you've got the second router since you've technically got 3 networks (10.x, 172.x and t'internet). However, normsherer is right, you could get away with just one router. It all depends on the physical locations of the machines.
Anyway, back to the problem at hand. Have you enabled ip forwarding on the routers?
Code:
echo 1 > /proc/sys/net/ipv4/ip_forward
Also, I assume it's a typo in router A's gateway specification (10.0.0.20?)
If the forwarding isn't the problem, post the result of running 'route -n' on all the machines. Enclose the results in [CODE] tags to make them readable.