Track / Stage 4 / 57 of 340 #317 of 2000

Problem 317

AMC 12 late, AIME early

Geometry Difficulty 4.6 Find the answer

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)

Your answer

Official solution

(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.)

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.