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 ?

A. \(\frac{2}{\sqrt{2} + 1}{\)

B. \(\frac{2}{\sqrt{2} - 1}{\)

C. \(\frac{2}{2\sqrt{2} + 1}{\)

D. \(\frac{\sqrt{2} + 1}{\sqrt{2} - 1}{\)

E. \(\frac{2\sqrt{2} + 1}{2\sqrt{2} - 1}{\)



OA D

Source: Official Guide