geometry
Circumcircle, circumcenter, and circumradius — AMC & AIME Problems
38 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Circumcircle, circumcenter, and circumradius — 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: Circumcenter and Circumcircle, Extended Law of Sines, Circumcenter and Circumcircle of Right Triangle.
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 21
- 1959 AMC 12 Problem 43
- 1960 AMC 12 Problem 15
- 1965 AMC 12 Problem 25
- 1966 AMC 12 Problem 31
- 1968 AMC 12 Problem 12
- 1973 AMC 12 Problem 15
- 1974 AMC 12 Problem 16
- 1977 AMC 12 Problem 19
- 1989 AMC 12 Problem 19
- 2003 AMC 12A Problem 11
- 2007 AMC 12A Problem 10
- 2011 AMC 12A Problem 25
- 2011 AMC 12B Problem 20
- 2015 AMC 12B Problem 19
- 2018 AMC 12B Problem 21
- 2021 AMC 12B Fall Problem 9
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
- 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