A purely geometric proof of the uniqueness of a triangle with prescribed angle bisectors - Victor Oxman We give a purely geometric proof of...
On the Nagel line and a prolific polar triangle - Jan Vonk For a given triangle ABC, the polar triangle of the medial triangle with respect to...
Second-degree involutory symbolic substitutions - Clark Kimberling Suppose a,b,c are algebraic indeterminates. The mapping (a,b,c) -> (bc,ca,ab)...
Some identities arising from inversion of Pappus chains in an arbelos - Giovanni Lucca We consider the inversive images, with respect to the...
Another compass-only construction of the golden section and of the regular pentagon - Michel Bataille We present a compass-only construction of...
A new proof of a weighted Erdos-Mordell type inequality - Yu-Dong Wu In this short note, by making use of one of Liu's theorems and...
Stronger forms of the Steiner-Lehmus theorem - Mowaffaq Hajja We give a short proof based on Breusch's lemma of a stronger form of the...
On the generalized Gergonne point and beyond - Miklos Hoffmann and Sonja Gorjanc In this paper we further extend the generalization of the...
Two more Powerian pairs in the arbelos - Quang Tuan Bui We construct two more pairs of Archimedes circles analogous to those of Frank Power, in...
Another variation of the Steiner-Lehmus theme - Sadi Abu-Saymeh, Mowaffaq Hajja, and Hassan Ali ShahAli Let the internal angle bisectors BB' and...
On the centroids of polygons and polyhedra - Maria Flavia Mammana, Biagio Micale and Mario Pennisi In this paper we introduce the centroid of any...
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Periodic billiard trajectories in polyhedra - Nicolas Bedaride We consider the billiard map inside a polyhedron. We give a condition for the...
A condition for a circumscriptible quadrilateral to be cyclic - Mowaffaq Hajja We give a short proof of a characterization, given by M. Radic et...
Means as chords - Francisco Javier Garcia Capitan On the circumcircle of a right triangle, we display chords whose lengths are the quadratic,...
A short proof of Lemoine's theorem - Cosmin Pohoata We give a short proof of Lemoine's theorem that the Lemoine point of a triangle is the unique...
Cubics related to coaxial circles - Bernard Gibert This note generalizes a result of Paul Yiu on a locus associated with a triad of coaxial...
An inequality involving the angle bisectors and an interior point of a triangle - Wei-Dong Jiang We establish a new weighted geometric inequality...
Haruki's lemma and a related locus problem - Yaroslav Bezverkhnyev In this paper we investigate the nature of the constant in Haruki's Lemma and...
A simple ruler and rusty compass construction of the regular pentagon - Kurt Hofstetter We construct in 13 steps a regular pentagon with given...
