geometry
Median (geometry) — AMC & AIME Problems
45 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.
LIVE focuses on challenge. As a social enterprise, we also explain standard school concepts one at a time, for free, on our sister site Expii. For this idea: Medians and Mid-Segments, Length Ratios Along Medians, Area Ratios from Medians and Centroid.
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.
AMC 10
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
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