MathDB

2

Part of 1902 Eotvos Mathematical Competition

Problems(1)

area of surface of a sphere inside another sphere is fixed

Source: Eotvos 1902 p2

9/6/2024
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.
geometry3D geometrysphere