7. Among all triangles with a fixed angle $A$ and a fixed inradius $r$, determine which triangle has the smallest perimeter.
(12th Canadian Mathematical Olympiad)
(Tip: Convert the comparison of perimeters into the comparison of areas. Answer: When $\triangle A B C$ is an isosceles triangle, with $\angle A$ as the vertex angle, the perimeter of $\triangle A B C$ is minimized.)