Pentagon's Constant

Geometry Level pending

The side of a regular pentagon is 1 1 unit . The sum of the perpendiculars from a point inside the pentagon to the sides (or their extensions) is constant. The constant is :

4 5 ( 1 + 5 ) \frac{4}{5}(1 + \sqrt{5}) 5 4 ( 2 + 5 ) \frac{5}{4}(2 + \sqrt{5}) 5 4 ( 1 + 5 ) \frac{5}{4}(1 + \sqrt{5}) 4 5 ( 2 + 5 ) \frac{4}{5}(2 + \sqrt{5})

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