Tangent circles — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Tangent circles — 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 8
AMC 10
2002 AMC 10A Problem 5 • 2002 AMC 10B Problem 5 • 2004 AMC 10A Problem 23 • 2004 AMC 10B Problem 16 • 2006 AMC 10A Problem 16 • 2006 AMC 10B Problem 24 • 2007 AMC 10A Problem 15 • 2007 AMC 10B Problem 18 • 2008 AMC 10A Problem 16 • 2009 AMC 10A Problem 6 • 2009 AMC 10A Problem 21 • 2012 AMC 10A Problem 11 • 2012 AMC 10B Problem 16 • 2014 AMC 10B Problem 22 • 2016 AMC 10A Problem 15 • 2016 AMC 10A Problem 21 • 2018 AMC 10A Problem 15 • 2019 AMC 10A Problem 16 • 2019 AMC 10B Problem 20 • 2021 AMC 10B Spring Problem 7 • 2022 AMC 10B Problem 22 • 2023 AMC 10A Problem 22 • 2024 AMC 10B Problem 21 • 2025 AMC 10A Problem 22 • 2025 AMC 10B Problem 12 • 2025 AMC 10B Problem 20
AMC 12
1954 AMC 12 Problem 26 • 1954 AMC 12 Problem 46 • 1959 AMC 12 Problem 41 • 1960 AMC 12 Problem 7 • 1965 AMC 12 Problem 39 • 1970 AMC 12 Problem 12 • 1971 AMC 12 Problem 35 • 1976 AMC 12 Problem 24 • 1976 AMC 12 Problem 26 • 1977 AMC 12 Problem 15 • 1978 AMC 12 Problem 26 • 1981 AMC 12 Problem 23 • 1983 AMC 12 Problem 23 • 1991 AMC 12 Problem 22 • 1993 AMC 12 Problem 8 • 1997 AMC 12 Problem 19 • 2000 AMC 12 Problem 24 • 2001 AMC 12 Problem 18 • 2002 AMC 12A Problem 5 • 2004 AMC 12A Problem 19 • 2005 AMC 12A Problem 16 • 2006 AMC 12A Problem 13 • 2006 AMC 12B Problem 15 • 2008 AMC 12A Problem 13 • 2009 AMC 12A Problem 16 • 2011 AMC 12A Problem 11 • 2011 AMC 12A Problem 17 • 2015 AMC 12A Problem 25 • 2016 AMC 12A Problem 15 • 2017 AMC 12A Problem 16 • 2018 AMC 12B Problem 21 • 2018 AMC 12B Problem 25 • 2019 AMC 12A Problem 10 • 2022 AMC 12B Problem 21 • 2023 AMC 12A Problem 18 • 2025 AMC 12A Problem 24
AIME
1991 AIME Problem 11 • 1992 AIME Problem 9 • 1995 AIME Problem 4 • 1997 AIME Problem 4 • 2002 AIME I Problem 2 • 2004 AIME II Problem 12 • 2005 AIME I Problem 1 • 2005 AIME II Problem 8 • 2005 AIME II Problem 15 • 2007 AIME I Problem 9 • 2008 AIME II Problem 11 • 2009 AIME II Problem 5 • 2014 AIME II Problem 8 • 2015 AIME II Problem 15 • 2017 AIME II Problem 12 • 2019 AIME I Problem 11 • 2019 AIME I Problem 15 • 2021 AIME I Problem 13 • 2022 AIME I Problem 8 • 2022 AIME II Problem 7 • 2024 AIME I Problem 8 • 2024 AIME II Problem 8 • 2025 AIME II Problem 6