3D geometry — AMC & AIME Practice Problems | LIVE by Po-Shen Loh

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3D geometry — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses 3D geometry — 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 of these problems are used with official legal permission of the Mathematical Association of America (MAA).

AMC 8

1991 AMC 8 Problem 15 · 1995 AMC 8 Problem 21 · 1998 AMC 8 Problem 21 · 1999 AMC 8 Problem 20 · 2002 AMC 8 Problem 22 · 2003 AMC 8 Problem 13 · 2003 AMC 8 Problem 15 · 2009 AMC 8 Problem 25 · 2026 AMC 8 Problem 15

AMC 10

2004 AMC 10A Problem 25 · 2006 AMC 10A Problem 24 · 2009 AMC 10B Problem 22 · 2010 AMC 10A Problem 17 · 2011 AMC 10A Problem 24 · 2012 AMC 10A Problem 21 · 2013 AMC 10A Problem 22 · 2014 AMC 10A Problem 19 · 2015 AMC 10A Problem 21 · 2020 AMC 10B Problem 20 · 2021 AMC 10A Spring Problem 13 · 2021 AMC 10A Fall Problem 22 · 2022 AMC 10A Problem 21 · 2023 AMC 10B Problem 20

More geometry concepts

altitude angle bisector angle bisector theorem angle chasing angle sum annulus arc area area decomposition area ratio Brahmagupta’s Formula centroid 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