On Collinear Feet of 0-lines of the Sides of a Triangle

Abstract

All angles considered in this paper are taken modulo Ï€. It is known that lines drawn through a point P on the circumcircle of a triangle A₁ A₂ A₃ making the same angle 0 in the same sense with the sides of the triangle meet the respective sides in collinear points (feet); the line of collinearity (called the 0-pedal line of P for A₁ A₂ A₃) is known to envelop, as P varies, a deltoid (called the 0-deltoid of A₁ A₂ A₃) touching the sides of the triangle.