Bulletin of Mathematics ISSN Printed: 2087-5126; Online: 2355-8202 Vol. 08, No. 01 (2016), pp. 81–96. http://jurnal.bull-math.org SOME RESULTS OF CONSTRUCTING SEMI GERGONNE POINT ON A NONCONVEX QUADRILATERAL Zukrianto, Mashadi, Sri Gemawati Abstract Suppose ABCD is a quadrilateral that is not convex. There are three pieces of semi-circular outer tangent and two pieces in a semi circle tangent of nonconvex quadrilateral. In this paper, it will be discussed how to calculate the length of the radius of the circle tangent quadrilateral that is not convex. Further discussion is how to calculate the length of the new sides that are formed by contructing the point of Semi Gergonne. 1. INTRODUCTION Two-dimensional figure of triangle is one of the scope of geometry that can always be constructed tangent circles inside and outside tangent circles [2, 8, 13, 14]. If a line is drawn from the third vertex of the triangle to the point of tangency of the circle in (incircle) then the third line will intersect at one point (concurrent), this is called Gergonne point inside the triangle and if there is a circle outside the triangle tangent (excircle) with the center point of tangency circle outside the triangle (excenter), it also can be formed Gergonne point outside the triangle derived from the circle tangent [1, 9, 13]. But this does not apply to the quadrilateral because not all rectangles can be constructed in a tangent circle and outer circle tangent. Circle tangent in the quadrilateral [4, 6, 12] is a circle inside a convex quadrilateral and Received 02-07-2016, Accepted 19-07-2016. 2010 Mathematics Subject Classification : 32B25, 51N15 Keywords and Phrases: quadrilateral, circle tangent, semi gergonne point 81 brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Talenta Publisher (E-Journals, Universitas Sumatera Utara)