My cat lost a large patch of fur on its neck, bare skin, but acts normal, eats and drinks, no pain; just noticed it today

Bald, broken, red skin on the chest area, from the photo, looks like a thermal or friction external injury, but bacterial infection, allergy, or eczema are also possible. A skin cytology at the vet confirms the type and speeds healing.

If a vet is not possible, rinse and disinfect the surface with iodine or hydrogen peroxide at home and apply an antibacterial ointment or spray. If the cat licks or scratches, fit an Elizabethan collar and keep the wound dry and away from water.

For simple external or bacterial injury, it improves in one to two weeks after scabbing. If not, see a vet.