Library / United States competition problems /22 of 37

United States competition problems

Geometry Difficulty 4.8 AIME Prove it United States

Problem:
Let $(x, y)$ be a point in the cartesian plane, $x, y > 0$ . Find a formula in terms of $x$ and $y$ for the minimal area of a right triangle with hypotenuse passing through $(x, y)$ and legs contained in the $x$ and $y$ axes.

Solution

Solution:
$2 x y$ .

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.