# A 108-gon is too much to figure out

**Geometry**Level 3

Given \({ A }_{ 1 }{ A }_{ 2 }{ A }_{ 3 }{ ...A }_{ 108 }\) be the equilateral 108-gon which in scribe the circle which has 1 cm radius. P is the point on the circle which is not the vertices of 108-gon. Then find \(\overline { { PA }_{ 1 } } ^{ 2 }+\overline { { PA }_{ 2 } } ^{ 2 }+\overline { { PA }_{ 3 } } ^{ 2 }+...+\overline { { PA }_{ 108 } } ^{ 2 }\)