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area of surface of a sphere inside another sphere is fixed

Source: Eotvos 1902 p2

September 6, 2024
geometry3D geometrysphere

Problem Statement

Let SS be a given sphere with center OO and radius rr. Let PP be any point outside then sphere SS, and let S′S' be the sphere with center PP and radius POPO. Denote by FF the area of the surface of the part of S′S' that lies inside SS. Prove that FF is independent of the particular point PP chosen.
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