Some Collinearities in the Heptagonal Triangle

نویسندگان

  • Abdilkadir Altintaş
  • A. Altintaş
چکیده

With the methods of barycentric coordinates, we establish several collinearities in the heptagonal triangle, formed by a side and two diagonals of different lengths of a regular heptagon. 1. The regular heptagon Consider a regular heptagon AA′C ′A′′BCB′ inscribed in a circle, each side of length a. The diagonals are of two kinds. Those with 3 vertices on the defining minor arc have the same length b, and those with 4 vertices on the defining minor arc have the same length c. There are seven of each kind. The lengths a, b, c satisfy some simple relations. Lemma 1. (a) a2 = c(c− b), (b) b2 = a(c+ a), (c) c2 = b(a+ b), (d) 1 a = 1 b + 1 c .

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تاریخ انتشار 2016