Problem 429: Circumscribed and Inscribed Regular Pentagon,
Perpendicular, Measurement. Level: High School, College, SAT Prep.
In the figure, a is the side of a
regular pentagon ABCDE circumscribed to circle O and b is the
side of a regular pentagon A'B'C'D'E' 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 c is the side of the pentagon A''B''C''D''E'', prove that
.

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