Variance of Topics of Plane Geometry

This book contains 21 papers of plane geometry.

It deals with various topics, such as: quasi-isogonal cevians,

nedians, polar of a point with respect to a circle, anti-bisector,

aalsonti-symmedian, anti-height and their isogonal.

A nedian is a line segment that has its origin in a triangle’s vertex

and divides the opposite side in n equal segments.

The papers also study distances between remarkable points in the

2D-geometry, the circumscribed octagon and the inscribable octagon,

the circles adjointly ex-inscribed associated to a triangle, and several

classical results such as: Carnot circles, Euler’s line, Desargues

theorem, Sondat’s theorem, Dergiades theorem, Stevanovic’s

theorem, Pantazi’s theorem, and Newton’s theorem.

Special attention is given in this book to orthological triangles, biorthological

triangles, ortho-homological triangles, and trihomological

triangles.

Each paper is independent of the others. Yet, papers on the same or similar

topics are listed together one after the other.

The book is intended for College and University students and instructors that

prepare for mathematical competitions such as National and International

Mathematical Olympiads, or for the AMATYC (American Mathematical

Association for Two Year Colleges) student competition, Putnam competition,

Gheorghe Ţiţeica Romanian competition, and so on.

The book is also useful for geometrical researchers.