2. 外语
  3. The figure above shows 2 circles．The larger circle has center A，radius R cm．and is inscribed in a square．The smaller circle has

The figure above shows 2 circles．The larger circle has center A，radius R cm．and is inscribed in a square．The smaller circle has

admin2022-10-18  66
问题
The figure above shows 2 circles．The larger circle has center A，radius R cm．and is inscribed in a square．The smaller circle has center C，radius r cm，and is tangent to the larger circle at point B and to the square at points D and F，If points A，B，C，and E are collinear，which of the following is equal to R/r?
选项 A、 
B、 
C、 
D、 
E、 
答案D
解析 Because is a diagonal of square CDEF, which has side length r, it follows from the Pythagorean an theorem that r2 + r2 = (CE)2, and hence CE = .
Therefore, BE= and AE = R + . Since 2(AE) is the diagonal length of the large square, which has side length 2R，it follows from the above tip that 2(AE) = (2R), or AE = R. Alternatively, an appropriate application of the Pythagorean theorem gives R2 + R2 = (AE)2, or AE = R.
Now substitute for AE and solve for R/r.

From the last equation we get
The correct answer is D.
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