math-ai/BlueMO
BlueMO 🚀 BlueMO: A Comprehensive Collection of Challenging Mathematical Olympiad Problems from the Little Blue Book Series BlueMO is a comprehensive and challenging dataset comprising mathematical olympiad problems paired with detailed solutions, meticulously curated from the esteemed "Little Blue Book" (小蓝书) series (Second Edition)—a vital resource for Chinese students training for national and international olympiad math competitions. Designed to… See the full description on the dataset page: https://huggingface.co/datasets/math-ai/BlueMO.
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1{2 "source_file": "./raw_volume-zh/volume4/exercise2.tex",3 "problem_type": "calculation",4 "problem": "问题23. 在所有周长一定的三角形中,求内切圆半径最大的三角形.",5 "solution": "设 $a 、 b 、 c$ 是半周长 $p$ 一定的三角形的边长, $S$ 与 $r$ 是它的面积与内切圆半径.\n则由平均值不等式, 得 $(r p)^2=S^2=p(p-a)(p-b)(p-c) \\leqslant p\\left[\\frac{(p-a)+(p-b)+(p-c)}{3}\\right]^3=\\frac{p^4}{27}$. 由此得到 $r \\leqslant \\frac{p}{\\sqrt{27}}$, 当且仅当 $p- a=p-b=p-c$, 即三角形为等边三角形时, $r$ 取到最大值.",6 "remark": "",7 "figures": []8}