geometry
Vector — AMC & AIME Problems
56 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Vector — 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: What Are Vectors and Components?, Operations with Vectors, Dot Products of Vectors.
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
- 1959 AMC 12 Problem 40
- 1961 AMC 12 Problem 36
- 1962 AMC 12 Problem 15
- 1963 AMC 12 Problem 38
- 1964 AMC 12 Problem 17
- 1967 AMC 12 Problem 37
- 1970 AMC 12 Problem 28
- 1975 AMC 12 Problem 28
- 1978 AMC 12 Problem 28
- 1978 AMC 12 Problem 29
- 1980 AMC 12 Problem 9
- 1982 AMC 12 Problem 18
- 1982 AMC 12 Problem 21
- 1985 AMC 12 Problem 17
- 2001 AMC 12 Problem 20
- 2018 AMC 12B Problem 23
- 2019 AMC 12B Problem 18
- 2019 AMC 12B Problem 24
- 2021 AMC 12A Fall Problem 13
- 2022 AMC 12B Problem 14
- 2024 AMC 12A Problem 7
AIME
- 1983 AIME Problem 14
- 1986 AIME Problem 14
- 1987 AIME Problem 9
- 1988 AIME Problem 7
- 1989 AIME Problem 12
- 1989 AIME Problem 15
- 1990 AIME Problem 7
- 1991 AIME Problem 12
- 1991 AIME Problem 15
- 1993 AIME Problem 2
- 1994 AIME Problem 8
- 1995 AIME Problem 12
- 2000 AIME II Problem 8
- 2001 AIME I Problem 12
- 2003 AIME II Problem 14
- 2009 AIME I Problem 4
- 2011 AIME I Problem 2
- 2011 AIME I Problem 13
- 2011 AIME II Problem 13
- 2013 AIME I Problem 7
- 2013 AIME II Problem 4
- 2019 AIME II Problem 13
- 2020 AIME I Problem 15
- 2022 AIME I Problem 5
- 2023 AIME I Problem 12
- 2023 AIME I Problem 13
- 2023 AIME II Problem 12
- 2025 AIME I Problem 2
- 2025 AIME I Problem 12
- 2026 AIME I 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
- 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
- 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
- Viviani’s Theorem
- Volume