The method and examples of solving problems analogous to "the problem of three bisectors"

TL;DR

This paper introduces a method for solving geometric problems involving the existence of a triangle with specified two bisectors and a third element, such as an angle, side, height, median, or bisector.

Contribution

It proposes a novel approach to determine the existence of a triangle given two bisectors and one additional element, expanding the toolkit for geometric problem solving.

Findings

Method successfully determines the existence of such triangles.

Applicable to various configurations involving angles, sides, heights, medians, or bisectors.

Provides a systematic approach to a class of geometric problems.

Abstract

We suggest a method of solving the problem of existence of a triangle with prescribed two bisectors and one third element which can be taken as one of the angles, the sides, the heights or the medians, or the third bisector.