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lateral surface area of pyramid, sphere inscribed

Source: Polish MO Recond Round 1981 p6

September 9, 2024
geometry3D geometrysphere

Problem Statement

The surface areas of the bases of a given truncated triangular pyramid are equal to B1 B_1 and B2 B_2 . This pyramid can be cut with a plane parallel to the bases so that a sphere can be inscribed in each of the obtained parts. Prove that the lateral surface area of the given pyramid is (B1+B2)(B14+B24)2 (\sqrt{B_1} + \sqrt{B_2})(\sqrt[4]{B_1} + \sqrt[4]{B_2})^2 .
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