Znanstvenostruèni
èasopis Hrvatskog dru¹tva za geometriju i grafiku Scientific and Professional Journal 
 Filipe Bellio, Ronaldo Garcia, Dan Reznik(filipe.bellio.nobrega@gmail.com, ragarcia@ufg.br, dreznik@gmail.com)
ParabolaInscribed Poncelet Derived from the Bicentric FamilyWe study loci and properties of a Parabolainscribed family
of Poncelet polygons whose caustic is a focuscentered
circle. This family is the polar image of a special case of
the bicentric family with respect to its circumcircle. We
describe closure conditions, curious loci, and new conserved
quantities.

 Ronaldo Garcia, Liliana G. Gheorghe, Peter Moses, Dan Reznik (ragarcia@ufg.br, liliana@dmat.ufpe.br, moparmatic@gmail.com, dreznik@gmail.com)
Triads of Conics Associated with a TriangleWe revisit constructions based on triads of conics with foci
at pairs of vertices of a reference triangle. We nd that
their 6 vertices lie on wellknown conics, whose type we
analyze. We give conditions for these to be circles and/or
degenerate. In the latter case, we study the locus of their
center. 
 Boris Odehnal (boris.odehnal@uniak.ac.at)
Pencil of Frégier ConicsFor each point P on a conic c, the involution of right angles at P induces an elliptic involution on c whose center F is called the Frégier point of P. Replacing the right angles at P between assigned pairs of lines with an arbitrary angle f yields a projective mapping of lines in the pencil about P, and thus, on c. The lines joining corresponding points on c do no longer pass through a single point and envelop a conic f which can be seen as the generalization of the Frégier point and shall be called a generalized Frégier conic. By varying the angle, we obtain a pencil of generalized Frégier conics which is a pencil of the third kind. We shall study the thus defined conics and discover, among other objects, general Poncelet triangle families. Key words: conic, angle, projective mapping, Frégier
point, Frégier conic, Poncelet porism, envelope 
 Helmuth Stachel (stachel@dmg.tuwien.ac.at)
On A Triple of Projective BilliardsA projective billiard is a polygon in the real projective plane
with a circumconic and an inconic. Similar to the classical
billiards in conics, the intersection points between the extended sides of a projective billiard are located on a family
of conics which form the associated Poncelet grid. We extend the projective billiard by the inner and outer billiard
and disclose various relations between the associated grids
and the diagonals, in particular other triples of projective
billiards. 
 Hans Dirnböck, Gunter Weiss (weissgunter@gmx.at)
János Bolyai’s Angle Trisection RevisitedJ. Bolyai proposed an elegant recipe for the angle trisection via the intersection of the arcs of the unit circle with that of an equilateral hyperbola c. It seems worthwhile to investigate the geometric background of this recipe and use it as the basic idea for finding the n^{th} part of a given angle. In this paper, we shall apply this idea for the trivial case n = 4, and for 5. Following Bolyai in the case 5, one has to intersect the unit circle with cubic curve c. There, and in the cases n ≥5, we find only numerical solutions, which shows the limitation of Bolyai's method. Therefore, we propose another construction based on epicycloids inscribed to the unit circle. By this method is even possible to construct the (n/m )^{th} part of a given angle. Key words:
angle trisection, angle nsection, equilateral
hyperbola, cubic, epicycloid 
 Vladimir Volenec, Ema Jurkin, Marija ©imiæ Horvath (volenec@math.hr, ema.jurkin@rgn.unizg.hr, marija.simic@arhitekt.hr)
A complete quadrilateral in rectangular coordinatesA complete quadrilateral in the Euclidean plane is studied. The geometry of such quadrilateral is almost as rich as the geometry of a triangle, so there are lot of associated points, lines and conics. Hereby, the study was performed in the rectangular coordinates, symmetrically on all four sides of the quadrilateral with four parameters a, b, c, d. In this paper we will study the properties of some points, lines and circles associated to the quadrilateral. All these properties are well known, but here they are all proved by the same method. During this process, still some new results have appeared. Key words:
Euclidean plane, complete quadrilateral,
parabola 