Answer

I no longer remember. From what you describe, it brings to mind for me the reasoning of the Rif and Maimonides and those who follow them regarding the exemption for an ox’s tooth and foot in the public domain, and perhaps also the exemption for an innocuous horn-goring animal everywhere. The reasoning is that the owner of the animal has permission to have it walk in the public domain, and the injured party must be careful. That does not exist in the case of a cheetah. There is no permission to walk with one in the public domain. By the way, the permission to walk in the public domain is not contingent on its being tied up and guarded. Quite the opposite: the animal walks there on its own, and even so the person is exempt. So we are not talking about someone who took his beloved cheetah out for a stroll in the public domain, but rather someone who sent his beloved cheetah to take a walk there by itself, to the delight of the public.
Even where we live, it is accepted that there is no legal permission to keep animals other than a dog or cat, especially dangerous ones. After all, even in one’s own home we maintain that there is a prohibition against keeping a dangerous dog (although it seems that this is a prohibition and not a liability to pay damages, and this is obvious because there it is my own property, so the duty of caution still rests on whoever enters).