Question 32
Let $a$, $b$, $c$ be the sides of a triangle, and $T$ its area. Prove that
$$
a^2 + b^2 + c^2 \ge 4\sqrt{3}T + (a-b)^2 + (b-c)^2 + (c-a)^2.
$$
When does the equality hold?
$$
a^2 + b^2 + c^2 \ge 4\sqrt{3}T + (a-b)^2 + (b-c)^2 + (c-a)^2.
$$
When does the equality hold?