A hawk rarely goes after prey as large as a mature cat. Even a large red-tailed hawk weighs in at only 2-3 pounds while a mature cat might weigh 12-15 pounds. An eagle? Maybe.
I watched my neighbor's cat and a red-tailed hawk get into a tif this summer in my back yard. Apparently the hawk dropped a dead pigeon and landed in the yard to pick it up and didn't see the cat on my deck. Some feathers were lost but both survived. In fact, the hawk stuck around until after the cat left so that it could collect its pigeon

Large bird. I sat on the deck while it perched on my fence not more than 20 feet away and watched me for a good 5 minutes...no doubt wondering whether or not I was a threat to it.