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Surface area on sphere

Source: Romanian TST 1979 day 2 P4

April 15, 2023
geometry3D geometrysphere

Problem Statement

Let A1A2A3A4A_1A_2A_3A_4 be a tetrahedron. Consider the sphere centered at A1A_1 which is tangent to the face A2A3A4A_2A_3A_4 of the tetrahedron. Show that the surface area of the part of the sphere which is inside the tetrahedron is less than the area of the triangle A2A3A4A_2A_3A_4.
Sorin Rădulescu
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