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3D problem on Moscow geometry olympiad

Source: Oral Moscow Geometry Olympiad 2024, 10-11.2

September 3, 2024
geometry3d

Problem Statement

Petya drew a pentagon ABCDEABCDE on the plane. After that, Vasya marked all the points SS in a given half-space relative to the plane of the pentagon so that in the pyramid SABCDSABCD exactly two side faces are perpendicular to the plane of the base ABCDABCD, and the height is 11. How many points could have Vasya?
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