39-RegularPentagon

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You may drag any of the red points, and the construction will adjust accordingly.

** Explanation of the construction: **

Back to ruler and compass constructions main page. The construction is based on the fact that sin(18°) = (sqrt(5)-1)/4. By the Pythagorean Theorem, HC = sqrt(5)/2 ,so CI = sqrt(5)/2 - 1/2. Thus chord CJ subtends 36°.

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