Question 4
(CZS 2) Let $T_1$ be a triangle having $a,b,c$ as lengths of its sides and let $T_2$ be another triangle having $u,v,w$ as lengths of its sides. If $P,Q$ are the areas of the two triangles, prove that
$$16PQ\le a^2(-u^2+v^2+w^2)+b^2(u^2-v^2+w^2)+c^2(u^2+v^2-w^2).$$
When does equality hold?
$$16PQ\le a^2(-u^2+v^2+w^2)+b^2(u^2-v^2+w^2)+c^2(u^2+v^2-w^2).$$
When does equality hold?