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Section of a regular tetragonal pyramid

Source: Sharygin contest. The final raund. 2008. Grade 10. First day. Problem 5

August 31, 2008
geometry3D geometrypyramidratiogeometry unsolved

Problem Statement

(I.Bogdanov) A section of a regular tetragonal pyramid is a regular pentagon. Find the ratio of its side to the side of the base of the pyramid.