geometry
Angle bisector theorem — AMC & AIME Problems
33 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Angle bisector theorem — 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: Angle Bisector Theorem, Proof of Angle Bisector Theorem.
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
- 1953 AMC 12 Problem 28
- 1959 AMC 12 Problem 28
- 1961 AMC 12 Problem 31
- 1965 AMC 12 Problem 30
- 1966 AMC 12 Problem 11
- 1967 AMC 12 Problem 21
- 1975 AMC 12 Problem 26
- 1981 AMC 12 Problem 25
- 1983 AMC 12 Problem 19
- 2000 AMC 12 Problem 17
- 2000 AMC 12 Problem 19
- 2002 AMC 12A Problem 23
- 2008 AMC 12A Problem 20
- 2009 AMC 12B Problem 16
- 2010 AMC 12A Problem 14
- 2016 AMC 12A Problem 12
- 2016 AMC 12B Problem 17
- 2018 AMC 12A Problem 18
- 2018 AMC 12B Problem 12
- 2025 AMC 12A Problem 8
More geometry concepts
- 3D geometry
- Altitude
- Angle bisector
- 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
- 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