Circumcircle, circumcenter, and circumradius — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses circumcircle, circumcenter, and circumradius — 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 10

2003 AMC 10A Problem 17 · 2004 AMC 10B Problem 22 · 2007 AMC 10B Problem 4 · 2007 AMC 10B Problem 11 · 2015 AMC 10B Problem 19 · 2019 AMC 10A Problem 6 · 2021 AMC 10A Fall Problem 15 · 2023 AMC 10B Problem 3 · 2025 AMC 10B Problem 5

More geometry concepts

3D geometryaltitudeangle bisectorangle bisector theoremangle chasingangle sumannulusarcareaarea decompositionarea ratioBrahmagupta’s Formulacentroidchordcirclecircle areacircumferenceconecongruence (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