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AMC geometry problems

Triangles and circles, polygons, coordinate geometry, area and similarity, solids, transformations and trigonometry.

897 problems in the archive use these ideas — 421 from the AMC 10 and 476 from the AMC 12.

Picks a problem you have not seen, at about the difficulty you are handling.

Narrow it down

  • Triangles379

    Triangle area, the Pythagorean theorem, special right triangles, medians, altitudes and angle bisectors.

  • Circles243

    Circle area and circumference, arcs and sectors, chords, tangents, inscribed angles and cyclic quadrilaterals.

  • Polygons & Quadrilaterals234

    Rectangles, trapezoids, parallelograms, regular polygons, angle chasing and perimeter.

  • Coordinate Geometry216

    Slope, the distance formula, midpoints, lattice points and conics in the coordinate plane.

  • Area & Similarity258

    Area decomposition, area ratios, similar figures, and how length, area and volume scale.

  • Solid Geometry135

    Volume and surface area of prisms, cylinders, cones, spheres and pyramids.

  • Transformations40

    Reflections, rotations and other transformations of the plane.

  • Trigonometry93

    Trigonometric identities and the laws of sines and cosines.

60 most recent problems

Newest contests first. Every problem opens with its answer choices, hints and a worked solution.

Use Start geometry practice above to keep going through the remaining 837, or browse them by contest in the AMC 12 and AMC 10 archives.