Similarity — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Similarity — 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.

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AMC 8

1994 AMC 8 Problem 16 1999 AMC 8 Problem 25 2002 AMC 8 Problem 20 2016 AMC 8 Problem 22 2017 AMC 8 Problem 22 2018 AMC 8 Problem 20 2018 AMC 8 Problem 22 2023 AMC 8 Problem 19 2023 AMC 8 Problem 24 2025 AMC 8 Problem 18

AMC 12

1950 AMC 12 Problem 47 1951 AMC 12 Problem 29 1953 AMC 12 Problem 12 1954 AMC 12 Problem 29 1956 AMC 12 Problem 26 1957 AMC 12 Problem 18 1957 AMC 12 Problem 35 1957 AMC 12 Problem 37 1958 AMC 12 Problem 19 1958 AMC 12 Problem 42 1958 AMC 12 Problem 47 1958 AMC 12 Problem 50 1959 AMC 12 Problem 2 1960 AMC 12 Problem 15 1960 AMC 12 Problem 37 1962 AMC 12 Problem 16 1963 AMC 12 Problem 18 1964 AMC 12 Problem 29 1965 AMC 12 Problem 8 1965 AMC 12 Problem 12 1965 AMC 12 Problem 36 1966 AMC 12 Problem 40 1967 AMC 12 Problem 15 1967 AMC 12 Problem 21 1967 AMC 12 Problem 29 1968 AMC 12 Problem 18 1971 AMC 12 Problem 28 1972 AMC 12 Problem 13 1972 AMC 12 Problem 18 1973 AMC 12 Problem 8 1974 AMC 12 Problem 23 1977 AMC 12 Problem 2 1979 AMC 12 Problem 28 1979 AMC 12 Problem 30 1980 AMC 12 Problem 26 1981 AMC 12 Problem 23 1982 AMC 12 Problem 10 1982 AMC 12 Problem 14 1983 AMC 12 Problem 23 1983 AMC 12 Problem 24 1983 AMC 12 Problem 27 1983 AMC 12 Problem 28 1984 AMC 12 Problem 17 1984 AMC 12 Problem 27 1989 AMC 12 Problem 4 1999 AMC 12 Problem 2 2000 AMC 12 Problem 21 2001 AMC 12 Problem 22 2002 AMC 12A Problem 18 2003 AMC 12B Problem 14 2004 AMC 12B Problem 14 2006 AMC 12A Problem 16 2007 AMC 12B Problem 22 2008 AMC 12B Problem 11 2009 AMC 12A Problem 20 2013 AMC 12A Problem 9 2013 AMC 12B Problem 19 2013 AMC 12B Problem 24 2014 AMC 12B Problem 12 2016 AMC 12B Problem 21 2017 AMC 12A Problem 19 2017 AMC 12A Problem 24 2017 AMC 12B Problem 14 2017 AMC 12B Problem 18 2017 AMC 12B Problem 24 2018 AMC 12A Problem 8 2018 AMC 12A Problem 11 2021 AMC 12A Spring Problem 10 2021 AMC 12A Spring Problem 17 2021 AMC 12B Fall Problem 24 2025 AMC 12B Problem 15

More geometry concepts

3D geometryaltitudeangle bisectorangle bisector theoremangle chasingangle sumannulusarcareaarea decompositionarea ratioBrahmagupta’s FormulaBritish Flag TheoremcentroidCeva’s Theoremchordcirclecircle areacircumcircle, circumcenter, and circumradiuscircumferenceconecongruence (geometry)coordinate geometrycube geometrycyclic quadrilateralcylinderdiagonaldistance formulaellipseequiangular polygonequilateral triangleEuler’s Polyhedron FormulaHeron’s Formulahomothetyhyperbolaincircle, incenter, and inradiusinscribed angleisosceles trianglekitelattice pointlaw of cosineslaw of sinesmass pointsmedian (geometry)midpointnet (3D geometry)paper foldingparabolaparallel linesparallelogramperimeterperpendicular bisectorPick’s Theorempolyhedronpower of a pointpower scaling of length, area, and volumePtolemy’s TheorempyramidPythagorean TheoremPythagorean Tripleradical axisrectanglerectangular prismreflection (geometry)regular polygonrhombusright trianglesectorshoelace formulaspecial right trianglespheresquare (geometry)Stewart’s Theoremsurface areatangent circlestangent linetransformationtrapezoidtriangle areatriangle inequalitytrigonometric identitytrigonometryvectorViviani’s Theoremvolume