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This page uses JavaSketchpad. You may drag any of the red points, and the construction will adjust accordingly.

Explanation of the construction:

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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