Centroid — AMC & AIME Problems | LIVE by Po-Shen Loh

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Centroid — AMC & AIME Problems

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

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.

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AMC 10

2004 AMC 10A Problem 25 • 2013 AMC 10B Problem 16 • 2017 AMC 10B Problem 24 • 2018 AMC 10B Problem 12 • 2020 AMC 10A Problem 12

AMC 12

1957 AMC 12 Problem 26 • 1961 AMC 12 Problem 21 • 1962 AMC 12 Problem 15 • 1965 AMC 12 Problem 16 • 1966 AMC 12 Problem 38 • 1967 AMC 12 Problem 37 • 1968 AMC 12 Problem 7 • 1970 AMC 12 Problem 28 • 1975 AMC 12 Problem 23 • 1976 AMC 12 Problem 22 • 1988 AMC 12 Problem 16 • 2004 AMC 12A Problem 22 • 2007 AMC 12B Problem 22 • 2016 AMC 12A Problem 17 • 2018 AMC 12B Problem 8 • 2018 AMC 12B Problem 13 • 2019 AMC 12B Problem 25 • 2022 AMC 12B Problem 19

AIME

1986 AIME Problem 15 • 1988 AIME Problem 11 • 2002 AIME I Problem 13 • 2003 AIME II Problem 4 • 2003 AIME II Problem 6 • 2013 AIME II Problem 4 • 2018 AIME II Problem 9 • 2021 AIME II Problem 14

More geometry concepts

3D geometry altitude angle bisector angle bisector theorem angle chasing angle sum annulus arc area area decomposition area ratio Brahmagupta’s Formula British Flag Theorem Ceva’s Theorem chord circle circle area circumcircle, circumcenter, and circumradius circumference cone congruence (geometry)coordinate geometry cube geometry cyclic quadrilateral cylinder diagonal distance formula ellipse equiangular polygon equilateral triangle Euler’s Polyhedron Formula Heron’s Formula homothety hyperbola incircle, incenter, and inradius inscribed angle isosceles triangle kite lattice point law of cosines law of sines mass points median (geometry)midpoint net (3D geometry)paper folding parabola parallel lines parallelogram perimeter 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 special right triangle 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