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在三角形中,有一个熟知的不等式命题为命题1 若△ABC的三边的长分别为a、b、c,外接圆半径为R,则 1986年,文[1]在圆内接四边形中,推出了一个类似的命题: 命题2 若圆内接四边形ABCD的四边长长分别为a、b、c、d,圆的半径为R,则 1987年,文[2]将上述命题一般化,进一步证明了命题3 若圆内接n边形A_1A_2…A_n的n边的长分别为a_1、a_2 …、a_n,圆的半径为R,则等号当且仅当A_1A_2……A_n为正n边形时成立。
In the triangle, there is a well-known inequality proposition as proposition 1. If the lengths of the three sides of △ABC are a, b, and c, and the radius of the circumscribed circle is R, then in 1986, the text [1] is in the circle inscribed in a quadrilateral, A similar proposition was introduced: Proposition 2 If the lengths of the four sides of the circle inscribed quadrilateral ABCD are a, b, c, and d, and the radius of the circle is R, in 1987, the article [2] generalized the above propositions, further Prove the proposition 3 If the length of the n-edges of the circle inscribed n-sided A_1A_2...A_n are a_1, a_2 ..., a_n respectively, and the radius of the circle is R, the equal sign if and only if A_1A_2... A_n is a positive n-gon Established.