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

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Perpendicular bisector — AMC & AIME Problems

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

2011 AMC 10B Problem 20 • 2015 AMC 10B Problem 19 • 2018 AMC 10A Problem 13 • 2019 AMC 10B Problem 23 • 2023 AMC 10A Problem 19

AMC 12

1957 AMC 12 Problem 46 • 1962 AMC 12 Problem 25 • 1963 AMC 12 Problem 10 • 1965 AMC 12 Problem 35 • 1970 AMC 12 Problem 20 • 1972 AMC 12 Problem 13 • 1977 AMC 12 Problem 19 • 1984 AMC 12 Problem 4 • 1991 AMC 12 Problem 29 • 2002 AMC 12A Problem 23 • 2002 AMC 12B Problem 18 • 2008 AMC 12B Problem 9 • 2011 AMC 12B Problem 16 • 2015 AMC 12B Problem 24 • 2018 AMC 12A Problem 11

AIME

1983 AIME Problem 4 • 1994 AIME Problem 15 • 1997 AIME Problem 4 • 2017 AIME I Problem 10 • 2017 AIME II Problem 3 • 2024 AIME I Problem 5 • 2025 AIME I Problem 8

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 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