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This is consistent with ringworm -- which is a simple fungal infection that comes from soil. It is contagious to people -- so I would care to wash my hands after handling this kitty. This can be treated with fungal cream -- but cats are often so effective at removing the cream that a systemic treatment (oral) is often more effctive.
This can be diagnosed by culture -- but frequently will be diagnosed by response to treatment.
Other possible reasons for this could be
1) Allergy with rubbing of the nose due to itching -- often see other areas of skin issues as well
2) Autoimmune disease -- would be diagnosed by appearance and biopsy
3) Mite -- need to do a skin scraping or biopsy
Considering the age of your cat, a vet visit would be the best way to treat this. You can attempt to use micaonazole cream (athletes foot fungal treatment) 3 times daily adn see if it is improving or not spreading in 7 days. IF it spreads further -- a vet visit is a necessity.
I hope this information helps!
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The above is given for information only. Although I am a licensed veterinarian, I cannot legally prescribe medicines or diagnose your pet's condition without performing a physical exam. If you have concerns about your pet I would highly advise contacting your regular veterinarian