geometry
Special right triangle — AMC & AIME Problems
59 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Special right triangle — 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: 45-45-90 Right Triangle: Side Ratios, 30-60-90 Right Triangle: Side Ratios.
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
- 2000 AMC 10 Problem 7
- 2001 AMC 10 Problem 20
- 2002 AMC 10B Problem 24
- 2003 AMC 10A Problem 17
- 2004 AMC 10B Problem 16
- 2004 AMC 10B Problem 25
- 2005 AMC 10A Problem 19
- 2005 AMC 10A Problem 20
- 2007 AMC 10A Problem 15
- 2007 AMC 10A Problem 19
- 2008 AMC 10A Problem 16
- 2008 AMC 10B Problem 14
- 2009 AMC 10B Problem 16
- 2010 AMC 10A Problem 14
- 2010 AMC 10B Problem 16
- 2010 AMC 10B Problem 20
- 2011 AMC 10B Problem 20
- 2012 AMC 10B Problem 12
- 2012 AMC 10B Problem 14
- 2013 AMC 10B Problem 7
- 2014 AMC 10A Problem 22
- 2015 AMC 10A Problem 19
- 2019 AMC 10B Problem 8
- 2020 AMC 10B Problem 21
- 2021 AMC 10B Spring Problem 20
- 2022 AMC 10A Problem 5
- 2024 AMC 10A Problem 14
- 2024 AMC 10A Problem 22
- 2025 AMC 10B Problem 13
AMC 12
- 1954 AMC 12 Problem 46
- 1957 AMC 12 Problem 31
- 1957 AMC 12 Problem 47
- 1966 AMC 12 Problem 6
- 1969 AMC 12 Problem 15
- 1973 AMC 12 Problem 4
- 1973 AMC 12 Problem 25
- 1974 AMC 12 Problem 16
- 1978 AMC 12 Problem 7
- 1980 AMC 12 Problem 5
- 1983 AMC 12 Problem 10
- 1984 AMC 12 Problem 8
- 1985 AMC 12 Problem 22
- 2001 AMC 12 Problem 24
- 2002 AMC 12A Problem 22
- 2008 AMC 12A Problem 13
- 2010 AMC 12A Problem 8
- 2010 AMC 12B Problem 13
- 2011 AMC 12B Problem 10
- 2016 AMC 12B Problem 13
- 2018 AMC 12B Problem 11
- 2018 AMC 12B Problem 25
- 2020 AMC 12B Problem 18
- 2025 AMC 12B Problem 10
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- Area ratio
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- British Flag Theorem
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- Heron’s Formula
- Homothety
- Hyperbola
- Incircle, incenter, and inradius
- Inscribed angle
- Isosceles triangle
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- Median (geometry)
- Midpoint
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- Perpendicular bisector
- Pick’s Theorem
- Polyhedron
- Power of a point
- Power scaling of length, area, and volume
- Ptolemy’s Theorem
- Pyramid
- Pythagorean Theorem
- Pythagorean Triple
- Radical axis
- Rectangle
- Rectangular prism
- Reflection (geometry)
- Regular polygon
- Rhombus
- Right triangle
- Sector
- Shoelace formula
- Similarity
- Sphere
- Square (geometry)
- Stewart’s Theorem
- Surface area
- Tangent circles
- Tangent line
- Transformation
- Trapezoid
- Triangle area
- Triangle inequality
- Trigonometric identity
- Trigonometry
- Vector
- Viviani’s Theorem
- Volume