Triangle inequality — AMC & AIME 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.
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
2000 AMC 10 Problem 10 • 2003 AMC 10A Problem 7 • 2006 AMC 10B Problem 10 • 2009 AMC 10A Problem 12 • 2010 AMC 10A Problem 16 • 2011 AMC 10B Problem 25 • 2013 AMC 10A Problem 23 • 2017 AMC 10A Problem 10 • 2019 AMC 10B Problem 10 • 2023 AMC 10A Problem 4 • 2025 AMC 10A Problem 3
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