benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let G be the centroid of triangle ABC. Find the biggest α such that there exists a triangle for which there are at least three angles among ∠GAB,∠GAC,∠GBA,∠GBC,∠GCA,∠GCB which are …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Let GG be the centroid of triangle ABCABC. Find the biggest α\alpha such that there exists a triangle for which there are at least three angles among ∠GAB,∠GAC,∠GBA,∠GBC,∠GCA,∠GCB\angle GAB, \angle GAC, \angle GBA, \angle GBC, \angle GCA, \angle GCB which are ≥α\geq \alpha.
Plain-text mathematical notation (without MathML)
Let G be the centroid of triangle ABC. Find the biggest α such that there exists a triangle for which there are at least three angles among ∠GAB,∠GAC,∠GBA,∠GBC,∠GCA,∠GCB which are ≥α.
Original LaTeX notation
Let $G$ be the centroid of triangle $ABC$. Find the biggest $\alpha$ such that there exists a triangle for which there are at least three angles among $\angle GAB, \angle GAC, \angle GBA, \angle GBC, \angle GCA, \angle GCB$ which are $\geq \alpha$.

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
cd22dfc1-f9b1-5105-9454-4004e871cbff
task_key
test--cd22dfc1-f9b1-5105-9454-4004e871cbff
task_revision_id
1
config / split
/ test

Official source

initial import