Which three of the following ancient facilities influenced modern facilities?

The Colosseum, Circus Maximus, and Hippodrome are pivotal examples of ancient facilities that have significantly influenced the design and function of modern sports venues.

The Colosseum, known for its grand scale and architectural ingenuity, served as a model for modern stadiums with its tiered seating, large capacity, and use of the central area for performances and contests. Its design has inspired contemporary amphitheaters and arenas, emphasizing spectator experience and functionality.

The Circus Maximus, primarily used for chariot racing, introduced the concept of large open spaces designed specifically for spectator sports. This ancient venue set precedents in terms of crowd management, viewing angles, and large-scale events, principles still essential in the design of modern racing tracks and sports stadiums.

The Hippodrome, also dedicated to horse racing, demonstrated early elements of what would become standard in modern arenas, such as elongated tracks suited for fast-paced competitions and grand spectator arrangements. Its design innovations concerning the allocation of space for athletes and audiences have informed ongoing practices in sports venue construction.

These three ancient sites collectively laid the groundwork for the aesthetic and functional elements we observe in contemporary sports facilities, making option B the most accurate choice.