benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Circle Ω has radius 5. Points A and B lie on Ω such that chord AB has length 6. A unit circle ω is tangent to chord AB at point T. Given that ω is also internally tangent to Ω, fin…

Problem

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

problem

Circle Ω\Omega has radius 5. Points AA and BB lie on Ω\Omega such that chord ABA B has length 6. A unit circle ω\omega is tangent to chord ABA B at point TT. Given that ω\omega is also internally tangent to Ω\Omega, find AT⋅BTA T \cdot B T.
Plain-text mathematical notation (without MathML)
Circle Ω has radius 5. Points A and B lie on Ω such that chord AB has length 6. A unit circle ω is tangent to chord AB at point T. Given that ω is also internally tangent to Ω, find AT⋅BT.
Original LaTeX notation
Circle $\Omega$ has radius 5. Points $A$ and $B$ lie on $\Omega$ such that chord $A B$ has length 6. A unit circle $\omega$ is tangent to chord $A B$ at point $T$. Given that $\omega$ is also internally tangent to $\Omega$, find $A T \cdot B T$.

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
441a680b-905d-54a0-8acf-4a9aadcf3ef4
task_key
test--441a680b-905d-54a0-8acf-4a9aadcf3ef4
task_revision_id
1
config / split
/ test

Official source

initial import