geometry
Chord — AMC & AIME Problems
59 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Chord — 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: Chord Length, Chords and the Center, Common Segment Products for Circles.
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
- 1952 AMC 12 Problem 29
- 1952 AMC 12 Problem 37
- 1957 AMC 12 Problem 18
- 1957 AMC 12 Problem 46
- 1958 AMC 12 Problem 21
- 1958 AMC 12 Problem 42
- 1963 AMC 12 Problem 18
- 1966 AMC 12 Problem 6
- 1966 AMC 12 Problem 8
- 1968 AMC 12 Problem 35
- 1969 AMC 12 Problem 6
- 1969 AMC 12 Problem 15
- 1971 AMC 12 Problem 31
- 1972 AMC 12 Problem 26
- 1973 AMC 12 Problem 1
- 1973 AMC 12 Problem 35
- 1975 AMC 12 Problem 11
- 1977 AMC 12 Problem 30
- 1980 AMC 12 Problem 19
- 1981 AMC 12 Problem 27
- 1982 AMC 12 Problem 14
- 1984 AMC 12 Problem 4
- 2003 AMC 12B Problem 25
- 2008 AMC 12B Problem 9
- 2012 AMC 12A Problem 16
- 2014 AMC 12A Problem 12
- 2014 AMC 12B Problem 24
- 2018 AMC 12B Problem 4
- 2020 AMC 12B Problem 12
- 2021 AMC 12B Spring Problem 8
- 2021 AMC 12A Fall Problem 11
- 2021 AMC 12B Fall Problem 10
- 2022 AMC 12B Problem 24
AIME
- 1983 AIME Problem 12
- 1983 AIME Problem 14
- 1983 AIME Problem 15
- 1985 AIME Problem 9
- 1990 AIME Problem 12
- 1991 AIME Problem 14
- 1994 AIME Problem 2
- 1994 AIME Problem 7
- 1995 AIME Problem 4
- 1995 AIME Problem 14
- 2001 AIME I Problem 13
- 2004 AIME II Problem 1
- 2005 AIME II Problem 8
- 2009 AIME II Problem 13
- 2011 AIME II Problem 10
- 2013 AIME II Problem 8
- 2017 AIME I Problem 8
- 2021 AIME I Problem 13
- 2022 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
- 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