A sailing vessel must display what if its sidelights are combined and shown on the fore and aft centerline?

When a sailing vessel combines its sidelights and displays them along the fore and aft centerline, it is required to show a combined lantern. This is important for visibility and identification on the water, allowing other vessels to clearly understand the direction and type of the sailing vessel.

The combined lantern effectively serves the purpose of side lights while ensuring that the vessel remains visible from all angles. This configuration is particularly useful in situations where space is limited or when a more streamlined lighting system is necessary. By using a combined lantern, the vessel adheres to maritime regulations that dictate proper lighting for navigation.

The other options do not satisfy the requirements for a sailing vessel displaying its sidelights. For example, a stern light is not sufficient on its own, as it does not indicate the lateral directionality needed for other vessels to safely navigate around the sailing vessel. Similarly, all-round white lights and only sidelights would also fail to convey the necessary information when the sidelights are combined. Thus, the correct answer is that a sailing vessel must display a combined lantern only when its sidelights are shown on the centerline.