An inequality between the area of a triangle inscribed in a given triangle and the harmonic mean of the areas of vertex triangles

ABSTRACT

In this article we consider two triangles: one inscribed in another. We prove that the area of the central triangle is at least the harmonic mean of the areas of corner triangles. We give two proofs of this theorem. One is based on Rigby inequality and the other is based on the known algebraic inequality, to which we bring a new, geometric, proof. The article can be used by teachers and students in courses on advanced classical geometry.

KEYWORDS:

• Triangle
• inequality
• harmonic mean

Disclosure statement

No potential conflict of interest was reported by the authors.