Question 144
Let $h$ be the altitude of triangle $ABC$ passing through the vertex $A$ and $\alpha = \angle BAC$. Prove that the following inequality holds:
$$
AB + AC \ge BC \cdot \cos \alpha + 2h \sin \alpha.
$$
In what triangles does equality hold?
$$
AB + AC \ge BC \cdot \cos \alpha + 2h \sin \alpha.
$$
In what triangles does equality hold?