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Lengths involving regular pentagon and a point on its circumcircle

Source: 2017 Pan-African Shortlist - G3

May 5, 2019
geometrypentagoncircumcircle

Problem Statement

Let ABCDEABCDE be a regular pentagon, and FF some point on the arc ABAB of the circumcircle of ABCDEABCDE. Show that FDFE+FC=FB+FAFD=−1+52, \frac{FD}{FE + FC} = \frac{FB + FA}{FD} = \frac{-1 + \sqrt{5}}{2}, and that FD+FB+FA=FE+FCFD + FB + FA = FE + FC.
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