Median (geometry) — AMC & AIME Problems | LIVE by Po-Shen Loh

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Median (geometry) — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Median (geometry) — 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

2002 AMC 10B Problem 22 • 2013 AMC 10B Problem 16 • 2014 AMC 10A Problem 14 • 2020 AMC 10A Problem 12 • 2025 AMC 10B Problem 13

AMC 12

1950 AMC 12 Problem 49 • 1951 AMC 12 Problem 49 • 1957 AMC 12 Problem 1 • 1957 AMC 12 Problem 26 • 1958 AMC 12 Problem 43 • 1959 AMC 12 Problem 26 • 1959 AMC 12 Problem 40 • 1961 AMC 12 Problem 10 • 1961 AMC 12 Problem 21 • 1961 AMC 12 Problem 36 • 1962 AMC 12 Problem 39 • 1964 AMC 12 Problem 38 • 1965 AMC 12 Problem 16 • 1966 AMC 12 Problem 32 • 1966 AMC 12 Problem 38 • 1968 AMC 12 Problem 7 • 1970 AMC 12 Problem 28 • 1973 AMC 12 Problem 9 • 1975 AMC 12 Problem 20 • 1975 AMC 12 Problem 28 • 1982 AMC 12 Problem 21 • 1989 AMC 12 Problem 7 • 2002 AMC 12B Problem 20 • 2002 AMC 12B Problem 23 • 2009 AMC 12A Problem 14 • 2012 AMC 12A Problem 10 • 2022 AMC 12A Problem 12 • 2022 AMC 12B Problem 19 • 2024 AMC 12A Problem 7 • 2024 AMC 12B Problem 20 • 2025 AMC 12B Problem 10

AIME

1986 AIME Problem 15 • 1996 AIME Problem 13 • 2003 AIME II Problem 11 • 2004 AIME I Problem 4 • 2005 AIME I Problem 10 • 2005 AIME I Problem 15 • 2008 AIME II Problem 5 • 2013 AIME II Problem 13 • 2017 AIME II Problem 15

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 centroid 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 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