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max no of points of a line, <AXC=1/2<BXC or <BXC =12<AXC

Source: Sharygin Finals 2022 10.3

October 26, 2022
geometryequal anglescombinatorial geometry

Problem Statement

A line meets a segment ABAB at point CC. Which is the maximal number of points XX of this line such that one of angles AXCAXC and BXCBXC is equlal to a half of the second one?
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