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Area of a Triangle in a Hexagon

Source:

March 16, 2010
geometrysymmetryrotation

Problem Statement

Suppose convex hexagon HEXAGN \text{HEXAGN} has 120∘ 120^\circ-rotational symmetry about a point P P—that is, if you rotate it 120∘ 120^\circ about P P, it doesn't change. If PX\equal{}1, find the area of triangle △GHX \triangle{GHX}.
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