Virtue Ethics and the Categorical Imperative

I once asked my Ethical Theory professor (great class by the way): are virtue ethics and the categorical imperative really contradictory, or are they just different?  He said they were, in fact, contradictory, but I remain skeptical.

A contradiction is not between A and B, but between A and ~A.  Let's take an example of virtue ethics and see how a Kantian might respond.  In virtue ethics, the golden mean between cowardice and rashness is bravery.  Bravery is exhibited when the risk carries a consequence whose benefits outweigh the costs.  For example, going into a burning house when there are people inside, and the house is not imminently at risk of collapsing.  Cowardice would be standing by and doing nothing.  Rashness would be going in even though there's no chance of the "hero" or anyone else escaping.

According to the categorical imperative (which is really just a fancy way of describing the Golden Rule: do unto others as you would have them do unto you), only those actions should be taken if they can be universalized.  Is it not the case that the right thing to do according to the categorical imperative is the exact same action suggested by virtue ethics?

I'm not saying there are no incompatibilities between the two ethical theories.  Nevertheless, I think the similarities greatly outnumber the incompatibilities.