Question 49
Suppose $a$, $b$, $c$ are the side lengths of an isosceles triangle $ABC$ with area $\Delta$. Prove that
$$
\sqrt{a^2 + b^2 - 4\Delta} + \sqrt{a^2 + c^2 - 4\Delta} \ge \sqrt{b^2 + c^2 - 4\Delta}.
$$
Determine the cases of equality.
$$
\sqrt{a^2 + b^2 - 4\Delta} + \sqrt{a^2 + c^2 - 4\Delta} \ge \sqrt{b^2 + c^2 - 4\Delta}.
$$
Determine the cases of equality.