A sufficient condition for reciprocal Jacobi triangles

Abstract

Given a triangle ABC let A B C be a Jacobi triangle for ABC. When ∠BA C = ∠CA B = α , ∠AB C = ∠CB A = β and ∠AC B = ∠BC A = γ , the triangle ABC is a Jacobi triangle for A B C . In this case we say that ABC and A B C are reciprocal Jacobi triangles. In 2015, G.T. Vickers presented a necessary condition for two triangles to be reciprocal, but the question whether that condition was also sufficient remained open. In this work we prove it by using basically trigonometric relations.