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P.o.t.W. #19

Problem of the Week #19

■  No GDC  ■

The figure shows an outer regular pentagon and a smaller inner regular pentagon that is shaded.

Find the ratio of the area of the outer pentagon to the area of the inner pentagon and express it exactly in the form \(\dfrac{{a + b\sqrt c }}{d}\) where \(a\), \(b\), \(c\) and \(d\) are different prime numbers.

[ Note: A polygon is regular when all sides are equal length and all angles are equal measure ]

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