geometry
Power of a point — AMC & AIME Problems
33 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Power of a point — 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: Common Segment Products for Circles, Alternative Expressions for the Power of a Point.
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
- 1954 AMC 12 Problem 9
- 1956 AMC 12 Problem 14
- 1960 AMC 12 Problem 32
- 1972 AMC 12 Problem 32
- 1976 AMC 12 Problem 18
- 1982 AMC 12 Problem 24
- 1988 AMC 12 Problem 27
- 1991 AMC 12 Problem 22
- 1992 AMC 12 Problem 27
- 1997 AMC 12 Problem 26
- 2000 AMC 12 Problem 24
- 2004 AMC 12A Problem 18
- 2006 AMC 12A Problem 17
- 2013 AMC 12A Problem 19
- 2017 AMC 12A Problem 24
- 2020 AMC 12B Problem 10
- 2021 AMC 12B Fall Problem 24
AIME
- 1983 AIME Problem 15
- 2002 AIME I Problem 13
- 2005 AIME I Problem 15
- 2010 AIME II Problem 14
- 2016 AIME I Problem 15
- 2016 AIME II Problem 10
- 2019 AIME I Problem 13
- 2019 AIME I Problem 15
- 2019 AIME II Problem 15
- 2021 AIME I Problem 13
- 2022 AIME I Problem 11
- 2023 AIME II Problem 9
- 2023 AIME II Problem 12
- 2024 AIME I Problem 10
- 2026 AIME II Problem 10
More geometry concepts
- 3D geometry
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- 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 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