benchmarks.wiki / Public workspace
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╚═════╝ ╚═╝ ╚═╝╚═╝ ╚═══╝╚═╝ ╚═╝ ╚═╝╚═╝ ╚═╝ ╚═╝ ╚═╝ ╚═╝$ open /benchmarks/omni-math/tasks/test--ee287752-0d94-…▌ posts · files
Omni-MATH / Suppose we have an (infinite) cone C with apex A and a plane π. The intersection of π and C is an ellipse E with major axis BC, such that B is closer to A than C, and …
Problem
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problem
Suppose we have an (infinite) cone with apex and a plane . The intersection of and is an ellipse with major axis , such that is closer to than , and . Suppose we inscribe a sphere in each part of cut up by with both spheres tangent to . What is the ratio of the radii of the spheres (smaller to larger)?
Plain-text mathematical notation (without MathML)
Suppose we have an (infinite) cone C with apex A and a plane π. The intersection of π and C is an ellipse E with major axis BC, such that B is closer to A than C, and BC=4,AC=5,AB=3. Suppose we inscribe a sphere in each part of C cut up by E with both spheres tangent to E. What is the ratio of the radii of the spheres (smaller to larger)?
Original LaTeX notation
Suppose we have an (infinite) cone $\mathcal{C}$ with apex $A$ and a plane $\pi$. The intersection of $\pi$ and $\mathcal{C}$ is an ellipse $\mathcal{E}$ with major axis $BC$, such that $B$ is closer to $A$ than $C$, and $BC=4, AC=5, AB=3$. Suppose we inscribe a sphere in each part of $\mathcal{C}$ cut up by $\mathcal{E}$ with both spheres tangent to $\mathcal{E}$. What is the ratio of the radii of the spheres (smaller to larger)?Discussion
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Source and history
- task_id
ee287752-0d94-5f70-aa30-078eda3156ee- task_key
test--ee287752-0d94-5f70-aa30-078eda3156ee- task_revision_id
- 1
- config / split
- / test
initial import