Which event is designed to showcase the athletic ability of a ranch type horse in a show arena?

The correct choice for showcasing the athletic ability of a ranch-type horse in a show arena is reining. Reining is a western riding competition that involves a horse demonstrating various maneuvers, including stops, spins, and circles, which not only highlight its athleticism but also its responsiveness and training.

Barrel racing is primarily focused on speed and maneuverability, as horses navigate around barrels in a timed event, while dressage emphasizes precision and training in a series of predefined movements, showcasing obedience and finesse rather than athletic ability specific to ranch-type horses. Jumping, on the other hand, is an English discipline where horses must clear obstacles, which involves a different skill set than that demonstrated by ranch-type horses typically seen in reining events.