Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 4.7 AIME Prove it Soviet Union

Problem:
The triangle $ABC$ satisfies $0 \leq AB \leq 1 \leq BC \leq 2 \leq CA \leq 3$ . What is the maximum area it can have?

Solution

Solution:
If we ignore the restrictions of $CA$ , then the maximum area is $1$ , achieved when $AB$ is perpendicular to $BC$ . But in this case $CA$ satisfies the restrictions.

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