Question 4
(BUL 4) Suppose medians $m_a$ and $m_b$ of a triangle are orthogonal. Prove that:
(a) The medians of that triangle correspond to the sides of a right-angled triangle.
(b) The inequality $$5(a^2+b^2-c^2)\geq8ab$$ is valid, where $a,b,c$ are side lengths of the given triangle.
(a) The medians of that triangle correspond to the sides of a right-angled triangle.
(b) The inequality $$5(a^2+b^2-c^2)\geq8ab$$ is valid, where $a,b,c$ are side lengths of the given triangle.