we just all look similar

The other day I had a patient asked me if I knew this Asian friend of his who also works at the hospital I work at. He said I reminded him of her. This happens a lot. People from time to time ask me if I know certain Asians that live in town. I just don't know what to say to that. I told this patient I don't know his friend, but throughout the night, he would tell me his friendship with his Asian friend. At the end of my shift, he asked me again if I was sure I didn't know his friend, I finally said, "no, we just all look similar." I wasn't trying to be rude, but I thought that would an end to that conversation, and it did.