geometry
Sector — AMC & AIME Problems
48 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Sector — 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: Area of a Sector, Arc Lengths, Types, and Names.
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
- 2001 AMC 10 Problem 17
- 2002 AMC 10A Problem 19
- 2003 AMC 10A Problem 19
- 2003 AMC 10B Problem 19
- 2004 AMC 10A Problem 21
- 2004 AMC 10B Problem 9
- 2004 AMC 10B Problem 25
- 2005 AMC 10A Problem 12
- 2006 AMC 10A Problem 12
- 2006 AMC 10B Problem 19
- 2007 AMC 10A Problem 24
- 2007 AMC 10B Problem 13
- 2008 AMC 10A Problem 17
- 2008 AMC 10B Problem 19
- 2010 AMC 10B Problem 16
- 2011 AMC 10A Problem 18
- 2012 AMC 10A Problem 18
- 2012 AMC 10B Problem 16
- 2012 AMC 10B Problem 17
- 2013 AMC 10A Problem 20
- 2014 AMC 10A Problem 12
- 2015 AMC 10B Problem 9
- 2017 AMC 10A Problem 22
- 2019 AMC 10B Problem 20
- 2020 AMC 10B Problem 14
- 2024 AMC 10A Problem 14
- 2025 AMC 10A Problem 25
AMC 12
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
- 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