IMO 2002 Problem 2a: Euclidean-geometry translation
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Let O be the midpoint of BC and let A lie on the circle with center O through B. Choose D on that circle with DA=DB. Let E and F be its intersections with the perpendicular bisector of OA, and let J=AC∩ℓ, where ℓ passes through O parallel to AD. Prove the directed line-angle equality ∠(EC,EJ)=∠(EJ,EF).
This page concerns the specialized translated task used in the IMO-AG-30 benchmark. The study’s aggregate result does not establish whether this individual task was solved.
Why it matters and what counts as progress
Why it matters: This is the first of two angle identities in the specialized circle-and-perpendicular-bisector configuration.
What counts as progress: A proof of the E-centered angle identity under the translated constructions, independently of the companion C-centered task.
How the problem developed
International Mathematical Olympiad Published the original IMO 2002 Problem 2a geometry problem at the annual contest. The AG30 file later gives its specialized translated statement.
Trieu H. Trinh and coauthors Included a translated version in the 30-problem AlphaGeometry benchmark; the study reports 25/30 solved overall, which does not identify this task’s individual result.
- 2025 · Problem level benchmark [4]
Yuri Chervonyi and coauthors Figure 8 of the AlphaGeometry 2 study lists the original IMO 2002 Problem 2a as the chart groups Problem 2; it does not distinguish 2a; for Problem 2, the chart does not separate the translated 2a and 2b tasks.
AI contribution
AlphaGeometry solves 25 translated Olympiad geometry problems
AlphaGeometry solved 25/30 specialized IMO-AG-30 classical Euclidean geometry translations using learned auxiliary-point constructions plus a symbolic deduction and algebra engine; the paper does not claim all natural-language IMO geometry conditions are represented.
Sources
- IMO 2002 official problem statement booklet
- Google DeepMind, AlphaGeometry 30 translated problem statements
- AlphaGeometry study and benchmark results
- Chervonyi et al., Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2
- Trinh and collaborators: Solving olympiad geometry without human demonstrations
- AlphaGeometry source and proof artifacts
- DeepMind account of computer checking
- Precise translated question and assumptions
Website timeline
Publication dates and editorial changes.
AlphaGeometry solves 25 translated Olympiad geometry problems