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Poncelet and the arquimedean twins
Liliana Gabriela Gheorghe
We give a sharp construction for twins in arbelos, based on polar reciprocity. In the process, new circles displaying arquimedean afinities came into scene.
Fine proprieties of Lemoine point and the inscribed conic
Liliana Gabriela Gheorghe
The center of an inscribed conic which have a given perspector is the complement of its isotomic conjugate. We provide a synthetic proof, based on fine proprieties of Lemoine point…
Exploring the Steiner-Soddy Porism
Ronaldo Garcia, Liliana Gheorghe, Dan Reznik
We explore properties and loci of a Poncelet family of polygons -- called here Steiner-Soddy -- whose vertices are centers of circles in the Steiner porism, including conserved qua…
Poristic virtues of a negative pedal curve
L. G. Gheorghe
We describe all triangles that shares either circumcircle and pedal circle or circumcircle and negative-pedal circle. Neither of these pairs is poristic; nevertheless, the negative…
When Euler (circle) meets Poncelet (Porism)
Liliana Gabriela Gheorghe
We describe all triangles that shares the same circumcircle and Euler circle. Although this two circles do not form a poristic pair of circles, we find a poristic circle "in-betwee…