On the Tucker circles - Sandor N. Kiss and Paul Yiu Parametrizing Tucker circles by the lengths of their antiparallel sides, we find conditions...
Regular polygons and the golden section - Djura Paunić and Paul Yiu Given an isosceles triangle and its circumcircle, we construct a chord...
Golden sections of triangle centers in the golden triangles - Emmanuel A. J. García and Paul Yiu A golden triangle is one whose vertices are...
The Kariya problem and related constructions - Paul Yiu Given a point Q other than the incenter I of a reference triangle, we give a simple conic...
Three constructions of Archimedean circles in an arbelos - Paul Yiu We give ruler and compass constructions of three Archimedean circles in an...
The touchpoints triangles and the Feuerbach hyperbolas - Sándor N. Kiss and Paul Yiu In this paper we generalize the famous Kariya theorem on the...
On the conic through the intercepts of the three lines through the centroid and the intercepts of a given line - Paul Yiu Let L be a line...
Sherman's fourth side of a triangle - Paul Yiu We give two simple ruler-and-compass constructions of the line which, like the sidelines of the...
The golden section with a collapsible compass only - Nikolaos Dergiades and Paul Yiu With the use of a collapsible compass, we divide a given...
Rational Steiner porism - Paul Yiu We establish formulas relating the radii of neighboring circles in a Steiner chain, a chain of mutually...
The circles of Lester, Evans, Parry, and their generalizations - Paul Yiu Beginning with the famous Lester circle containing the circumcenter,...
Reflections in triangle geometry - Antreas P. Hatzipolakis and Paul Yiu This paper is a survey of results on reflections in triangle geometry. We...
Heptagonal triangles and their companions - Paul Yiu A heptagonal triangle is a non-isosceles triangle formed by three vertices of a regular...
Construction of Malfatti squares - Floor van Lamoen and Paul Yiu We give a very simple construction of the Malfatti squares of a triangle, and...
On a product of two points induced by their cevian triangles - Cosmin Pohoata and Paul Yiu The intersections of the corresponding sidelines of...
Some constructions related to the Kiepert hyperbola - Paul Yiu Given a reference triangle and its Kiepert hyperbola K, we study several...
The Feuerbach point and Euler lines - Bogdan Suceava and Paul Yiu Given a triangle, we construct three triangles associated its incircle whose...
Elegant geometric constructions - Paul Yiu With the availability of computer software on dynamic geometry, beautiful and accurate geometric...
Antiparallels and concurrency of Euler lines - Nikolaos Dergiades and Paul Yiu We study the condition for concurrency of the Euler lines of the...
On the Fermat lines - Paul Yiu We study the triangle formed by three points each on a Fermat line of a given triangle, and at equal distances...
