Problem 430: Circumscribed and Inscribed Regular Pentagon,
Perpendicular, Areas. Level: High School, College, SAT Prep.
In the figure, ABCDE is a regular
pentagon circumscribed to circle O and A'B'C'D'E' is a regular
pentagon inscribed in circle O. Lines A'A''B', B'B''C'',
C'C''D'', D'D''E'', and E'E''A'' are perpendicular to A'E',
A'B', B'C', C'D', and D'E', respectively. If S is the area of
the green shaded region and S_{1} is the area of the
pentagon A''B''C''D''E'',

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