geometry
Triangle inequality — AMC & AIME Problems
58 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Triangle inequality — a geometry concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.
LIVE focuses on challenge. As a social enterprise, we also explain standard school concepts one at a time, for free, on our sister site Expii. For this idea: The Triangle Inequality and Degenerate Triangles.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.
AMC 10
AMC 12
- 1950 AMC 12 Problem 46
- 1952 AMC 12 Problem 15
- 1956 AMC 12 Problem 43
- 1963 AMC 12 Problem 35
- 1964 AMC 12 Problem 27
- 1966 AMC 12 Problem 35
- 1968 AMC 12 Problem 22
- 1969 AMC 12 Problem 11
- 1977 AMC 12 Problem 5
- 1979 AMC 12 Problem 17
- 1986 AMC 12 Problem 29
- 1988 AMC 12 Problem 23
- 1990 AMC 12 Problem 7
- 1990 AMC 12 Problem 27
- 1995 AMC 12 Problem 23
- 2003 AMC 12A Problem 7
- 2006 AMC 12B Problem 10
- 2009 AMC 12A Problem 10
- 2010 AMC 12A Problem 14
- 2011 AMC 12B Problem 22
- 2012 AMC 12B Problem 23
- 2013 AMC 12A Problem 24
- 2014 AMC 12B Problem 12
- 2014 AMC 12B Problem 13
- 2015 AMC 12A Problem 2
- 2015 AMC 12B Problem 10
- 2016 AMC 12A Problem 23
- 2017 AMC 12A Problem 6
- 2018 AMC 12B Problem 12
- 2019 AMC 12A Problem 19
- 2019 AMC 12B Problem 9
- 2024 AMC 12B Problem 20
- 2024 AMC 12B Problem 22
- 2024 AMC 12B Problem 24
- 2025 AMC 12B Problem 21
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