Which architectural element provides support and helps distribute weight in Gothic cathedrals?

The flying buttress is the correct answer because it is a distinctive architectural feature of Gothic cathedrals that was specifically designed to support the structure's walls and distribute the weight of the heavy stone ceilings and expansive stained glass windows. By transferring the thrust of the roof outward and down to the ground, flying buttresses allowed Gothic architects to build taller and more open spaces than had been possible in earlier architectural styles. This innovation not only mitigated the effects of the building's weight on the walls but also enabled the inclusion of large windows that filled the interior with natural light, which is a hallmark of Gothic architecture.

Other elements listed, such as the tympanum, transept, and triforium, serve different functions within the structure. The tympanum typically refers to the decorative semi-circular or triangular space above doorways, often adorned with sculptures. The transept serves as the cross arm of a church, creating a cruciform plan, while the triforium is a tier of arcades or openings located between the arches of the nave and the clerestory. While important to the overall architecture, these elements do not provide the critical load-bearing support that makes the flying buttress so significant in Gothic design.