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. Inscribe a regular hexagon in the unit circle. Inscribe a regular dodecagon (12-gon) over the hexagon. Use special right triangles and the Pythagorean theorem

 . I̲n̲s̲c̲r̲i̲b̲e̲ ̲a̲ ̲r̲e̲g̲u̲l̲a̲r̲ ̲h̲e̲x̲a̲g̲o̲n̲ ̲i̲n̲ ̲t̲h̲e̲ ̲u̲n̲i̲t̲ ̲c̲i̲r̲c̲l̲e̲.̲ ̲I̲n̲s̲c̲r̲i̲b̲e̲ ̲a̲ ̲r̲e̲g̲u̲l̲a̲r̲ ̲d̲o̲d̲e̲c̲a̲g̲o̲n̲ ̲(̲1̲2̲-̲g̲o̲n̲)̲ ̲o̲v̲e̲r̲ ̲t̲h̲e̲ ̲h̲e̲x̲a̲g̲o̲n̲.̲ ̲U̲s̲e̲ ̲s̲p̲e̲c̲i̲a̲l̲ ̲r̲i̲g̲h̲t̲ ̲t̲r̲i̲a̲n̲g̲l̲e̲s̲ ̲a̲n̲d̲ ̲t̲h̲e̲ ̲P̲y̲t̲h̲a̲g̲o̲r̲e̲a̲n̲ ̲t̲h̲e̲o̲r̲e̲m̲ ̲t̲o̲ ̲f̲i̲n̲d̲ ̲i̲t̲s̲ ̲p̲e̲r̲i̲m̲e̲t̲e̲r̲.̲ ̲I̲f̲ ̲t̲h̲i̲s̲ ̲p̲e̲r̲i̲m̲e̲t̲e̲r̲ ̲i̲s̲ ̲a̲ ̲l̲o̲w̲e̲r̲ ̲b̲o̲u̲n̲d̲ ̲f̲o̲r̲ ̲π̲,̲ ̲c̲o̲m̲p̲u̲t̲e̲ ̲t̲h̲e̲ ̲e̲r̲r̲o̲r̲ ̲w̲i̲t̲h̲ ̲a̲ ̲c̲a̲l̲c̲u̲l̲a̲t̲o̲r̲.̲

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