Area ratio — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses area ratio — 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 of these problems are used with official legal permission of the Mathematical Association of America (MAA).

AMC 8

1991 AMC 8 Problem 25 · 1994 AMC 8 Problem 12 · 1994 AMC 8 Problem 16 · 1996 AMC 8 Problem 25 · 1997 AMC 8 Problem 15 · 1998 AMC 8 Problem 13 · 2002 AMC 8 Problem 20 · 2002 AMC 8 Problem 23 · 2007 AMC 8 Problem 12 · 2008 AMC 8 Problem 25 · 2010 AMC 8 Problem 10 · 2010 AMC 8 Problem 18 · 2010 AMC 8 Problem 23 · 2012 AMC 8 Problem 23 · 2017 AMC 8 Problem 16 · 2018 AMC 8 Problem 20 · 2018 AMC 8 Problem 22 · 2019 AMC 8 Problem 24 · 2020 AMC 8 Problem 24 · 2023 AMC 8 Problem 12 · 2023 AMC 8 Problem 19 · 2023 AMC 8 Problem 24

More geometry concepts

3D geometryaltitudeangle bisectorangle bisector theoremangle chasingangle sumannulusarcareaarea decompositionBrahmagupta’s Formulacentroidchordcirclecircle 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 formulasimilarityspecial right trianglespheresquare (geometry)Stewart’s Theoremsurface areatangent circlestangent linetransformationtrapezoidtriangle areatriangle inequalitytrigonometric identitytrigonometryvectorViviani’s Theoremvolume