Paris Pamfilios,
Self-Pivoting Convex Quadrangles,
Forum Geometricorum, 18 (2018) 321--347.
Abstract. In this article we examine conditions for
the existence of pivoting circumscriptions of a convex quadrangle q_1 by
another quadrangle q similar to q_1, pivoting about a
fixed point. There are 8 types of such circumscriptions and we formulate the
restrictions on the quadrangles of each type, imposed by the requirement of
such a circumscription. In most cases these restrictions imply that the
quadrangles are cyclic of a particular type, in one
case are harmonic quadrilaterals, and in two cases are trapezia of a special
kind.
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