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

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Sector — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Sector — 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

1987 AMC 8 Problem 22 • 2014 AMC 8 Problem 20 • 2017 AMC 8 Problem 25 • 2024 AMC 8 Problem 18

AMC 12

1952 AMC 12 Problem 37 • 1973 AMC 12 Problem 15 • 1973 AMC 12 Problem 25 • 1979 AMC 12 Problem 8 • 2003 AMC 12A Problem 15 • 2003 AMC 12B Problem 16 • 2004 AMC 12A Problem 24 • 2008 AMC 12B Problem 4 • 2012 AMC 12A Problem 14 • 2013 AMC 12A Problem 23

AIME

1995 AIME Problem 14 • 1999 AIME Problem 6 • 2004 AIME II Problem 1 • 2008 AIME II Problem 13 • 2010 AIME I Problem 13 • 2015 AIME I Problem 15 • 2019 AIME II Problem 13

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 Pythagorean Triple radical axis rectangle rectangular prism reflection (geometry)regular polygon rhombus right triangle 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