On the impossibility of constructing a triangle given its internal bisectors

2017/06/21 by A. Caminha, Caminha, Antonio, A.F. Maia +1
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #History and Overview (math.HO) #Mathematics and Applications #Primary 12F05 #Robotic Mechanisms and Dynamics #Secondary 12-01

paper · pdf · doi:10.48550/arxiv.1706.08508

openalex publication_date 2017/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a simple proof to the fact that it is impossible to use straightedge and compass to construct a triangle given the lengths of its internal bisectors, even if the triangle is isosceles.

Related

• On the construction of a triangle from the feet of its angle bisectors
• On existence of a triangle with prescribed bisector lengths
• A New Equilateral Triangle?
• No perfect triangle is isosceles
• The largest angle bisection procedure