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In geometric inequalities ADM mass plays more fundamental role than theconcept of quasi-local mass. This paper is to demonstrate that using thequasi-local mass some new insights can be acquired. In spherically symmetricspacetimes the Misner-Sharp mass and the concept of the Kodama vector fieldprovides an ideal setting to the investigations of geometric inequalities. Weapplying the proposed new techniques to investigate the spacetimes containingblack hole or cosmological horizons but we shall also apply them in context ofnormal bodies. Most of the previous investigations applied only the quasi-localcharges and the area. Our main point is to include the quasi-local mass in thecorresponding geometrical inequalities. This way we recover some knownrelations but new inequalities are also derived.

Geometric inequalities in spherically symmetric spacetimes