Math Contest Resources

Home AP Calculus AB Precalculus Honors Algebra II CPE
Math Tools
Interactive Explorers Desmos Applets Math Contest Resources AI Resources Visualizing Math
Past Courses
Calculus Honors Algebra II Advanced Precalculus I CP

Problem Archives

Contest Practice & Solutions

AMC 10/12 Problems & Solutions From Art of Problem Solving, a collection of AMC 10/12 problems and solutions.
Open archive
AIME Problems & Solutions From Art of Problem Solving, a collection of AIME problems and solutions.
Open archive
USAMO Problems & Solutions From Art of Problem Solving, a collection of USAMO problems and solutions.
Open archive
Mind Your Decisions Presh Talwalkar's mathematics and problem-solving site.
Visit site

Geometry Challenge

GaoKao 2025 ยท Problem 7

The circle \(x^2 + (y + 2)^2 = r^2\), where \(r > 0\), contains exactly two points whose distance from the line \(y = \sqrt{3}x + 2\) is \(1\). In which interval does \(r\) lie?

  • A \((0,1)\)
  • B \((1,3)\)
  • C \((3,+\infty)\)
  • D \((0,+\infty)\)
Solution coming soon

Puzzle Challenge

Overlapping Squares

The diagram shows four overlapping squares with side lengths 5, 7, 9, and 11. What is the difference between the total area shaded grey and the total area shaded black?

  1. A 25
  2. B 36
  3. C 49
  4. D 64
  5. E More information needed
Four overlapping grey and black squares with side lengths 11, 9, 7, and 5.
Top of Page Home