geometry
Arc — AMC & AIME Problems
41 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Arc — 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: Arc Lengths, Types, and Names, Central Angle Measure Equals Arc Measure, Inscribed Angle Theorem: Chord Case.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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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 8
AMC 10
AMC 12
- 1951 AMC 12 Problem 46
- 1952 AMC 12 Problem 43
- 1954 AMC 12 Problem 13
- 1958 AMC 12 Problem 15
- 1960 AMC 12 Problem 35
- 1963 AMC 12 Problem 22
- 1964 AMC 12 Problem 36
- 1965 AMC 12 Problem 2
- 1968 AMC 12 Problem 11
- 1969 AMC 12 Problem 8
- 1971 AMC 12 Problem 5
- 1972 AMC 12 Problem 26
- 1972 AMC 12 Problem 35
- 1977 AMC 12 Problem 9
- 1981 AMC 12 Problem 27
- 1983 AMC 12 Problem 30
- 1985 AMC 12 Problem 2
- 1989 AMC 12 Problem 19
- 2000 AMC 12 Problem 24
- 2001 AMC 12 Problem 8
- 2002 AMC 12A Problem 7
- 2003 AMC 12B Problem 25
- 2007 AMC 12A Problem 8
- 2011 AMC 12B Problem 6
- 2025 AMC 12A Problem 10
- 2025 AMC 12B Problem 12
More geometry concepts
- 3D geometry
- Altitude
- Angle bisector
- Angle bisector theorem
- Angle chasing
- Angle sum
- Annulus
- 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
- Vector
- Viviani’s Theorem
- Volume