No abstract

The sufficient and necessary condition for a circular annulus to have the property of Poncelet porism is given. Moreover, the family of annuli with a property of the Poncelet porism and some family of periodic functions are considered. The close relations between these families are given.

ABS fRAC]'. ]'he closed plane curves of class C 2 which have curvature k(s) > 0 or k(s) >I 0 with a finite number of zeros are studied. The results concern the existence of normal lines which divide the perimeter into equal parts and the existence of some special kinds of pairs of points on these curves as orthodiameter pairs, antipodal pairs, etc. The paper also contains some generalizations of the theorems of Blaschke-Siiss and Barbier.Geometriae Dedicata 2,t (1987) 221-228. !1) 1987 by D. Reidel Publishing Company.

In the present paper we describe the family of all closed convex plane curves of class $$C^1$$ C 1 which have circles as their isoptics. In the first part of the paper we give a certain characterization of all ellipses based on the notion of isoptic and we give a geometric characterization of curves whose orthoptics are circles. The second part of the paper contains considerations on curves which have circles as their isoptics and we show the form of support functions of all considered curves.