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exists cyclic quadrilateral, section of a pyramid with convex quadr. base?

Source: 2006 Oral Moscow Geometry Olympiad grades 10-11 p5

October 20, 2020
geometrycyclic quadrilateral3D geometrypyramid

Problem Statement

The base of the pyramid is a convex quadrangle. Is there necessarily a section of this pyramid that does not intersect the base and is an inscribed quadrangle?
(M. Volchkevich)