benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Circle Ω has radius 13. Circle ω has radius 14 and its center P lies on the boundary of circle Ω. Points A and B lie on Ω such that chord AB has length 24 and is tangent to ω at po…

Problem

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

problem

Circle Ω\Omega has radius 13. Circle ω\omega has radius 14 and its center PP lies on the boundary of circle Ω\Omega. Points AA and BB lie on Ω\Omega such that chord ABA B has length 24 and is tangent to ω\omega at point TT. Find AT⋅BTA T \cdot B T.
Plain-text mathematical notation (without MathML)
Circle Ω has radius 13. Circle ω has radius 14 and its center P lies on the boundary of circle Ω. Points A and B lie on Ω such that chord AB has length 24 and is tangent to ω at point T. Find AT⋅BT.
Original LaTeX notation
Circle $\Omega$ has radius 13. Circle $\omega$ has radius 14 and its center $P$ lies on the boundary of circle $\Omega$. Points $A$ and $B$ lie on $\Omega$ such that chord $A B$ has length 24 and is tangent to $\omega$ at point $T$. 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
16ff860d-8b81-5787-8db0-9ad710e22a71
task_key
test--16ff860d-8b81-5787-8db0-9ad710e22a71
task_revision_id
1
config / split
/ test

Official source

initial import