MathDB

Suppose, medians

m_a

and

m_b

of a triangle are orthogonal. Prove that: (a) The medians of the triangle correspond to the sides of a right-angled triangle. (b) If

a,b,c

are the side-lengths of the triangle, then, the following inequality holds:

5(a^2+b^2-c^2)\geq 8ab

Problem Statement