# Omni-MATH / 

task_id: af36bc7c-3bfa-5db1-9751-094cacb22f77
task_key: test--af36bc7c-3bfa-5db1-9751-094cacb22f77
task_revision_id: 1

{"problem":"Determine the smallest positive real number $ k$ with the following property. Let $ ABCD$ be a convex quadrilateral, and let points $ A_1$, $ B_1$, $ C_1$, and $ D_1$ lie on sides $ AB$, $ BC$, $ CD$, and $ DA$, respectively. Consider the areas of triangles $ AA_1D_1$, $ BB_1A_1$, $ CC_1B_1$ and $ DD_1C_1$; let $ S$ be the sum of the two smallest ones, and let $ S_1$ be the area of quadrilateral $ A_1B_1C_1D_1$. Then we always have $ kS_1\\ge S$.\n\n[i]Author: Zuming Feng and Oleg Golberg, USA[/i]"}

Source: https://huggingface.co/datasets/KbsdJames/Omni-MATH

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