Koundinya-Mathematics Teachers Hub

$The\,\,radius\,\,of\,\,the \,\, circle\,\,circumscribed\,\,about \,\,a\,\,regular\,\,n-gon\\A_1,\,A_2\,....A_n\,\, is\,\,equal\,\,to\,\,R, \,\, Prove\,\,that\\ (a)\,the\,\, sum\,\, of\,\, the\,\, squares\,\, of\,\, all\,\, sides\,\, and\,\, of\\ the\,\,squares\,\, of\,\, all\,\, diagonals\,\, of\,\, the\,\, n-gon\,\, is \,\,equal\,\, to\,\, n^2R^2\\ (b)\,the\,\, sum\,\, of\,\, all\,\, sides\,\, and\,\, of\,\, all\,\, diagonals\,\, of\,\, the\,\, n-gon\,\, is\\ equal\,\, to\,\,\,\, n\, cot(\pi R/2n)\\ (c)\,the\,\, product\,\, of\,\, all\,\, sides\,\, and\,\, of\,\, all\,\, diagonals\,\, of\,\, the\,\, n-gon \\is\,\, equal\,\, to\,\, n^{n/2}R^{n(n-1)/2}$

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