geometry
Incircle, incenter, and inradius — AMC & AIME Problems
53 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Incircle, incenter, and inradius — 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: Incenter and Incircle, Inradius, Semiperimeter, and Area, Inradius 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 12
- 1950 AMC 12 Problem 35
- 1954 AMC 12 Problem 19
- 1954 AMC 12 Problem 43
- 1957 AMC 12 Problem 7
- 1958 AMC 12 Problem 16
- 1963 AMC 12 Problem 15
- 1964 AMC 12 Problem 13
- 1966 AMC 12 Problem 31
- 1967 AMC 12 Problem 3
- 1967 AMC 12 Problem 5
- 1970 AMC 12 Problem 27
- 1974 AMC 12 Problem 16
- 1977 AMC 12 Problem 15
- 1979 AMC 12 Problem 21
- 1980 AMC 12 Problem 26
- 1982 AMC 12 Problem 10
- 1999 AMC 12 Problem 16
- 2008 AMC 12A Problem 20
- 2011 AMC 12A Problem 13
- 2011 AMC 12A Problem 24
- 2011 AMC 12B Problem 22
- 2012 AMC 12A Problem 18
- 2018 AMC 12B Problem 21
- 2019 AMC 12A Problem 18
- 2022 AMC 12A Problem 25
- 2024 AMC 12B Problem 24
AIME
- 1993 AIME Problem 15
- 1999 AIME Problem 12
- 2000 AIME II Problem 10
- 2001 AIME I Problem 7
- 2001 AIME I Problem 12
- 2001 AIME II Problem 7
- 2005 AIME I Problem 15
- 2007 AIME II Problem 9
- 2007 AIME II Problem 15
- 2009 AIME I Problem 12
- 2009 AIME I Problem 15
- 2010 AIME I Problem 15
- 2015 AIME I Problem 11
- 2016 AIME I Problem 6
- 2018 AIME I Problem 13
- 2018 AIME II Problem 14
- 2019 AIME I Problem 11
- 2020 AIME II Problem 13
- 2023 AIME I Problem 8
- 2024 AIME I Problem 8
- 2024 AIME II Problem 10
- 2025 AIME I Problem 6
- 2026 AIME II Problem 8
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
- 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