Right triangle — AMC & AIME Practice Problems | LIVE by Po-Shen Loh

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Right triangle — AMC & AIME Problems

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

2000 AMC 10 Problem 19 · 2002 AMC 10A Problem 13 · 2004 AMC 10B Problem 22 · 2006 AMC 10B Problem 24 · 2007 AMC 10A Problem 14 · 2007 AMC 10B Problem 21 · 2009 AMC 10A Problem 10 · 2009 AMC 10A Problem 17 · 2009 AMC 10B Problem 10 · 2015 AMC 10A Problem 21 · 2015 AMC 10B Problem 19 · 2017 AMC 10A Problem 21 · 2017 AMC 10B Problem 15 · 2017 AMC 10B Problem 21 · 2018 AMC 10A Problem 16 · 2018 AMC 10A Problem 23 · 2019 AMC 10B Problem 15 · 2020 AMC 10B Problem 8 · 2023 AMC 10B Problem 3

AMC 12

1999 AMC 12 Problem 21 · 2002 AMC 12B Problem 20 · 2004 AMC 12B Problem 14 · 2007 AMC 12A Problem 10 · 2007 AMC 12B Problem 23 · 2013 AMC 12A Problem 1 · 2014 AMC 12B Problem 21 · 2015 AMC 12A Problem 16 · 2015 AMC 12B Problem 11 · 2015 AMC 12B Problem 19 · 2017 AMC 12A Problem 19 · 2019 AMC 12B Problem 12 · 2023 AMC 12A Problem 15 · 2023 AMC 12B Problem 3 · 2024 AMC 12A Problem 10

AIME

2001 AIME II Problem 7 · 2004 AIME I Problem 4 · 2007 AIME I Problem 9 · 2008 AIME II Problem 5 · 2011 AIME I Problem 14 · 2012 AIME I Problem 14 · 2015 AIME I Problem 7 · 2019 AIME I Problem 3 · 2019 AIME I Problem 6

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 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 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