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一、问题的提出蔡兆生在《探究性课题——三角形的内接正方形的面积》(中学数学,2001年第7期)一文中研究表明:对于锐角三角形,内接正方形的一边落在锐角三角形最短边上时,裁出的正方形最大;对于直角三角形,内接正方形的一边落在任一直角边上时,裁出的正方形最大;对于钝角三角形,蔡兆生没有给出定论,认为从操作角度看,将内接正方形的一边落在钝角三角形较短边上具有应用价值.
First, the issue raised Cai Zhaosheng in the “Inquiry Project - the area of the inscribed square of the triangle” (high school mathematics, 2001 seventh period) study shows that: acute triangle, the inscribed side of the square falls sharp triangle shortest When the edge, the largest square cut out; for right-angled triangle, the inner side of the square falls on any right-angle edge, the largest square cut out; for the obtuse triangle, Cai Zhaosheng did not give a conclusion, that from the operational point of view, The inner side of the square falls on the shorter side of the obtuse triangle has an application value.