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

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Diagonal — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Diagonal — 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).

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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

1997 AMC 8 Problem 17 • 2001 AMC 8 Problem 7 • 2001 AMC 8 Problem 8 • 2017 AMC 8 Problem 11

AMC 10

2008 AMC 10A Problem 21

AMC 12

1950 AMC 12 Problem 45 • 1951 AMC 12 Problem 3 • 1952 AMC 12 Problem 39 • 1954 AMC 12 Problem 45 • 1959 AMC 12 Problem 3 • 1960 AMC 12 Problem 6 • 1960 AMC 12 Problem 21 • 1961 AMC 12 Problem 14 • 1962 AMC 12 Problem 6 • 1964 AMC 12 Problem 10 • 1975 AMC 12 Problem 4 • 1981 AMC 12 Problem 9 • 1984 AMC 12 Problem 25 • 1985 AMC 12 Problem 17 • 2002 AMC 12B Problem 24 • 2016 AMC 12A Problem 9

AIME

2004 AIME I Problem 3

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 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