# A 108-gon is too much to figure out

Geometry Level 3

Given $${ A }_{ 1 }{ A }_{ 2 }{ A }_{ 3 }{ ...A }_{ 108 }$$ be a regular 108-gon inscribed in a circle which has 1 cm radius. P is the point on the circle which is not one of the vertices of 108-gon. Then find $$\overline { { PA }_{ 1 } } ^{ 2 }+\overline { { PA }_{ 2 } } ^{ 2 }+\overline { { PA }_{ 3 } } ^{ 2 }+...+\overline { { PA }_{ 108 } } ^{ 2 }$$

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