Final answer:
The largest living platyrrhines belong to the family Atelidae, which includes large New World monkeys like the spider monkey and muriqui.
Step-by-step explanation:
The question asks about the family with the largest living platyrrhines, which are a clade of New World monkeys found in Central and South America. The Platyrrhini are part of the infraorder Simiiformes, under the larger suborder Haplorrhini, which also includes apes, humans, and other primates. Among the New World monkeys, the family Atelidae, which includes howler, spider, woolly monkeys, and muriquis, are known to have some of the largest species, such as the spider monkey and the muriqui. These monkeys are characterized by their prehensile tails, which act like an extra limb to help them navigate the tree canopy where they live.