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max area of Q, angle between 30^o and 60^o 2019 BMT Individual 5

Source:

January 5, 2022
geometryareasangles

Problem Statement

Point PP is 3\sqrt3 units away from plane AA. Let QQ be a region of AA such that every line through PP that intersects AA in QQ intersects AA at an angle between 30o30^o and 60o60^o . What is the largest possible area of QQ?
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