Distance formula — AMC & AIME Practice Problems | LIVE by Po-Shen Loh

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Distance formula — AMC & AIME Problems

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

1988 AMC 8 Problem 9

AMC 10

2000 AMC 10 Problem 16 · 2006 AMC 10B Problem 20 · 2012 AMC 10A Problem 21 · 2014 AMC 10A Problem 19 · 2017 AMC 10A Problem 17 · 2021 AMC 10A Spring Problem 24

AMC 12

2004 AMC 12A Problem 12 · 2004 AMC 12B Problem 18 · 2005 AMC 12B Problem 16 · 2006 AMC 12B Problem 16 · 2008 AMC 12B Problem 21 · 2011 AMC 12A Problem 15 · 2011 AMC 12B Problem 11 · 2013 AMC 12B Problem 11 · 2018 AMC 12A Problem 17 · 2020 AMC 12A Problem 2 · 2020 AMC 12A Problem 15 · 2021 AMC 12A Spring Problem 11 · 2021 AMC 12A Spring Problem 20 · 2021 AMC 12B Fall Problem 22 · 2022 AMC 12A Problem 13 · 2022 AMC 12B Problem 10

AIME

1997 AIME Problem 7 · 2001 AIME II Problem 4 · 2001 AIME II Problem 7 · 2002 AIME I Problem 15 · 2002 AIME II Problem 2 · 2004 AIME I Problem 10 · 2005 AIME I Problem 14 · 2006 AIME I Problem 14 · 2008 AIME II Problem 10 · 2008 AIME II Problem 14 · 2009 AIME II Problem 5 · 2010 AIME I Problem 8 · 2011 AIME I Problem 3 · 2015 AIME I Problem 4 · 2016 AIME I Problem 14 · 2021 AIME I Problem 6 · 2021 AIME I Problem 9 · 2025 AIME II Problem 1

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 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