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设D、E、F分别是△ABC的三边BC、CA、AB边上的点,若△DEF∽△ABC,则称△DEF为△ABC的内接相似三角形.文[1]给出了任意三角形与其内接三角形相似的一个充要条件,读后颇受启发,由此引发的、需要研究的问题是:三角形的内接相似三角形有多少个?三角形的内接相似三角形的周长与面积有无最大、最小值?本文研究这些问题.1任意三角形的内接相似三角形的个数
Let D, E, and F be the points on the three sides BC, CA, and AB of △ABC respectively. If △DEF ∽ △ABC, we call △DEF △ABC inscribed similar triangles. The paper [1] gives A necessary and sufficient condition for an arbitrary triangle to be similar to its intrinsic triangle is inspiring after reading it. The questions that need to be investigated are: How many triangles are connected to similar triangles? The intrinsic length of triangles is similar to that of triangles. Whether the area has the maximum or minimum value? This paper studies these problems.1 The number of intrinsic similar triangles of an arbitrary triangle