benchmarks.wiki / Public workspace

MATH / A circle is centered at (5,15) and has a radius of √(130) units. Point Q=(x,y) is on the circle, has integer coordinates, and the value of the x-coordinate is twice the value of th…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

A circle is centered at (5,15)(5,15) and has a radius of 130\sqrt{130} units. Point Q=(x,y)Q = (x,y) is on the circle, has integer coordinates, and the value of the xx-coordinate is twice the value of the yy-coordinate. What is the maximum possible value for xx?
Plain-text mathematical notation (without MathML)
A circle is centered at (5,15) and has a radius of √(130) units. Point Q=(x,y) is on the circle, has integer coordinates, and the value of the x-coordinate is twice the value of the y-coordinate. What is the maximum possible value for x?
Original LaTeX notation
A circle is centered at $(5,15)$ and has a radius of $\sqrt{130}$ units. Point $Q = (x,y)$ is on the circle, has integer coordinates, and the value of the $x$-coordinate is twice the value of the $y$-coordinate. What is the maximum possible value for $x$?

level

Level 5

type

Algebra

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

Official source

initial import