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Problems

Problems and solutions

Entries are organized by topic, method, and an editorial 1–10 difficulty scale. When a source statement cannot be republished, the archive presents the solution only and links to the source.

5 entries shown

Solution onlyDifficulty 6/10

A Solution to Crux Mathematicorum Problem 5021

A direct-similarity generalization proved with Pappus's theorem and a radical axis, presented without reproducing the original problem statement.

  • Projective geometry
  • Circles
  • Transformations
10 August 2026Read →
Solution onlyDifficulty 5/10

A Solution to Crux Mathematicorum Problem 5031

A concise incircle-inversion proof using contact-chord midpoints and a cyclic quadrilateral, presented without reproducing the original problem statement.

  • Triangle geometry
  • Circles
  • Transformations
10 August 2026Read →
Solution onlyDifficulty 6/10

A Solution to Crux Mathematicorum Problem 5088

A concise angle-chasing proof through tangency and cyclic quadrilaterals, presented without reproducing the original problem statement.

  • Circles
  • Triangle geometry
10 August 2026Read →
Solution onlyDifficulty 6/10

A Solution to Crux Mathematicorum Problem 5098

A unit-circle complex proof that reduces two geometric conditions to the same algebraic equation, presented without reproducing the original problem statement.

  • Triangle geometry
  • Circles
  • Algebra
10 August 2026Read →
Solution onlyDifficulty 5/10

A Solution to Crux Mathematicorum Problem 5109

A synthetic fixed-point argument and a projective generalization, presented without reproducing the original problem statement.

  • Triangle geometry
  • Projective geometry
  • Conics
10 August 2026Read →

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ELEMENTARY GEOMETRY

Problems, Proofs, and Diagrams

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English edition · 2026