benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / A regular octahedron ABCDEF is given such that AD,BE, and CF are perpendicular. Let G,H, and I lie on edges AB,BC, and CA respectively such that …ρ>1,GH,HI, and IG are three edges …

Problem

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

problem

A regular octahedron ABCDEFA B C D E F is given such that AD,BEA D, B E, and CFC F are perpendicular. Let G,HG, H, and II lie on edges AB,BCA B, B C, and CAC A respectively such that \frac{A G}{G B}=\frac{B H}{H C}=\frac{C I}{I A}=\rho. For some choice of ρ>1,GH,HI\rho>1, G H, H I, and IGI G are three edges of a regular icosahedron, eight of whose faces are inscribed in the faces of ABCDEFA B C D E F. Find ρ\rho.
Plain-text mathematical notation (without MathML)
A regular octahedron ABCDEF is given such that AD,BE, and CF are perpendicular. Let G,H, and I lie on edges AB,BC, and CA respectively such that \frac{A G}{G B}=\frac{B H}{H C}=\frac{C I}{I A}=\rho. For some choice of ρ>1,GH,HI, and IG are three edges of a regular icosahedron, eight of whose faces are inscribed in the faces of ABCDEF. Find ρ.
Original LaTeX notation
A regular octahedron $A B C D E F$ is given such that $A D, B E$, and $C F$ are perpendicular. Let $G, H$, and $I$ lie on edges $A B, B C$, and $C A$ respectively such that \frac{A G}{G B}=\frac{B H}{H C}=\frac{C I}{I A}=\rho. For some choice of $\rho>1, G H, H I$, and $I G$ are three edges of a regular icosahedron, eight of whose faces are inscribed in the faces of $A B C D E F$. Find $\rho$.

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
489f8c83-fe24-574a-808c-2cfb42cc7ac8
task_key
test--489f8c83-fe24-574a-808c-2cfb42cc7ac8
task_revision_id
1
config / split
/ test

Official source

initial import