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Geometry

Spring 2026 · 30 problems

Thirty problems in three parts: the basic facts, training exercises, and competition-level geometry. The most developed set in the archive.

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What is in it

Problems only — the club works these out together at meetings. Topic and attribution are listed as a starting point.

1. The Star's Points Euclidean GeometryEasy
2. Triangle Area by Coordinates Coordinate GeometryEasy
3. The Midline Theorem Euclidean / Vector Geometry
4. Varignon's Parallelogram Euclidean / Linear Algebra
5. Angles and Chords Circle Geometry
6. Power of a Point Circle Geometry
7. Ceva's Theorem Euclidean Geometry
8. Menelaus' Theorem Euclidean Geometry
9. The Shortest Path Euclidean Geometry
10. The Sliding Ladder Coordinate Geometry / Loci
11. The British Flag Theorem Coordinate Geometry
12. The Euler Line Vector Geometry
13. The Apollonius Circle Coordinate Geometry / Loci
14. Composition of Reflections Transformations / Group Theory
15. Napoleon's Theorem Geometry / Complex Numbers
16. Homothety and the Nine-Point Circle Transformations
17. Harmonic Division Projective Geometry
18. Ptolemy's Theorem Circle Geometry
19. The Simson Line Circle Geometry
20. The Isoperimetric Inequality for Triangles Optimization
21. The Envelope of a Sliding Rod Kinematic Geometry
22. The Butterfly Theorem Circle Geometry
23. Monge's Theorem Transformations / Homothety
24. Desargues' Theorem Projective Geometry
25. Langley's Adventitious Angles Euclidean GeometryE. M. Langley, Math. Gazette, 1922
26. No Equilateral Triangle on a Lattice Coordinate Geometry
27. Euler's Formula for \(OI\) Circle Geometry
28. The Erdos–Mordell Inequality Geometric InequalitiesP. Erdos, Amer. Math. Monthly, 1935
29. A Tangent and Two Chords Circle GeometryIMO 1990, Problem 1
30. An Implicit Lesson on Quadratic Forms Triangle GeometrySpelman College’s Problem of the Month February 2017