Pythagorean Triple — AMC & AIME Problems | LIVE by Po-Shen Loh

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Pythagorean Triple — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Pythagorean Triple — 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.

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.

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AMC 8

2003 AMC 8 Problem 6 • 2005 AMC 8 Problem 19 • 2011 AMC 8 Problem 20 • 2017 AMC 8 Problem 18 • 2026 AMC 8 Problem 3

AMC 10

2002 AMC 10A Problem 25 • 2003 AMC 10B Problem 6 • 2008 AMC 10B Problem 15 • 2013 AMC 10B Problem 16 • 2022 AMC 10A Problem 15 • 2023 AMC 10A Problem 17

AMC 12

1950 AMC 12 Problem 35 • 1967 AMC 12 Problem 40 • 1972 AMC 12 Problem 25 • 1981 AMC 12 Problem 11 • 2003 AMC 12B Problem 5 • 2008 AMC 12A Problem 9 • 2022 AMC 12A Problem 25 • 2022 AMC 12B Problem 13 • 2024 AMC 12B Problem 21

AIME

1994 AIME Problem 10 • 2007 AIME II Problem 3 • 2015 AIME II Problem 4 • 2016 AIME II Problem 5

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 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