International Journal of Computer Discovered Mathematics (IJCDM) ISSN 2367-7775 c IJCDM November 2015, Volume 0, No.0, pp.60-69. Received 15 July 2015. Published on-line 15 September 2015 web: http://www.journal-1.eu/ c The Author(s) This article is published with open access1. Computer Discovered Mathematics: Hexyl-Anticevian Triangles Sava Grozdeva and Deko Dekovb2 a VUZF University of Finance, Business and Entrepreneurship, Gusla Street 1, 1618 Sofia, Bulgaria e-mail:
[email protected] bZahari Knjazheski 81, 6000 Stara Zagora, Bulgaria e-mail:
[email protected] web: http://www.ddekov.eu/ Abstract. We introduce the notion of a Hexyl-anticevian triangle of a point P . The known Hexyl triangle coincides with the Hexyl-anticevian triangle of the Incenter. In this paper we present theorems about the Hexyl-anticevian triangle of a point P , and we also consider the special cases when P is the Incenter or the Centroid. All theorems and problems in this paper are discovered by the computer program “Discoverer”. Theorems about other special cases, e.g. when P is the Circumcenter, Orthocenter, Symmedian Point, and so on, could be easily discovered by the “Discoverer” upon request. Keywords. hexyl triangle, hexyl-antimedial triangle, triangle geometry, remark- able point, computer-discovered mathematics, Euclidean geometry, “Discoverer”. Mathematics Subject Classification (2010). 51-04, 68T01, 68T99. 1. Introduction The computer program “Discoverer”, created by the authors, is the first computer program, able easily to discover new theorems in mathematics, and possibly, the first computer program, able easily to discover new knowledge in science. See [4]. In this paper, by using the “Discoverer”, we investigate the hexyl-anticevian trian- gles.