geometry
Tangent line — AMC & AIME Problems
76 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Tangent line — 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: Tangents and Perpendicular Radii, Two Tangent Theorem.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
Filter by difficulty
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
- 2004 AMC 10A Problem 22
- 2004 AMC 10B Problem 12
- 2006 AMC 10A Problem 23
- 2007 AMC 10A Problem 24
- 2009 AMC 10B Problem 16
- 2010 AMC 10B Problem 20
- 2012 AMC 10A Problem 11
- 2014 AMC 10B Problem 19
- 2017 AMC 10A Problem 22
- 2019 AMC 10B Problem 23
- 2021 AMC 10A Fall Problem 15
- 2024 AMC 10A Problem 14
- 2024 AMC 10B Problem 14
- 2025 AMC 10A Problem 20
AMC 12
- 1951 AMC 12 Problem 16
- 1952 AMC 12 Problem 8
- 1954 AMC 12 Problem 26
- 1959 AMC 12 Problem 32
- 1960 AMC 12 Problem 32
- 1961 AMC 12 Problem 11
- 1962 AMC 12 Problem 25
- 1963 AMC 12 Problem 4
- 1964 AMC 12 Problem 13
- 1965 AMC 12 Problem 30
- 1966 AMC 12 Problem 40
- 1967 AMC 12 Problem 29
- 1969 AMC 12 Problem 10
- 1969 AMC 12 Problem 21
- 1971 AMC 12 Problem 9
- 1971 AMC 12 Problem 19
- 1974 AMC 12 Problem 23
- 1976 AMC 12 Problem 18
- 1976 AMC 12 Problem 26
- 1978 AMC 12 Problem 11
- 1982 AMC 12 Problem 14
- 1983 AMC 12 Problem 27
- 1984 AMC 12 Problem 29
- 1990 AMC 12 Problem 6
- 2000 AMC 12 Problem 17
- 2002 AMC 12A Problem 18
- 2004 AMC 12A Problem 18
- 2004 AMC 12B Problem 10
- 2004 AMC 12B Problem 19
- 2004 AMC 12B Problem 21
- 2005 AMC 12B Problem 14
- 2006 AMC 12A Problem 16
- 2006 AMC 12A Problem 17
- 2006 AMC 12A Problem 19
- 2011 AMC 12B Problem 6
- 2015 AMC 12A Problem 11
- 2019 AMC 12A Problem 22
- 2019 AMC 12B Problem 20
- 2021 AMC 12B Fall Problem 22
- 2023 AMC 12B Problem 21
AIME
- 1983 AIME Problem 15
- 1993 AIME Problem 13
- 1994 AIME Problem 7
- 2000 AIME I Problem 13
- 2002 AIME II Problem 14
- 2002 AIME II Problem 15
- 2004 AIME I Problem 14
- 2005 AIME I Problem 11
- 2006 AIME II Problem 9
- 2008 AIME I Problem 14
- 2009 AIME I Problem 12
- 2014 AIME I Problem 7
- 2018 AIME II Problem 14
- 2019 AIME II Problem 11
- 2020 AIME II Problem 13
- 2020 AIME II Problem 15
- 2022 AIME I Problem 11
- 2022 AIME II Problem 7
- 2024 AIME I Problem 10
- 2025 AIME I Problem 8
- 2026 AIME II Problem 6
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