Problem Solving

The figure above shows \(2\) circles. The larger circle has center \(A,\) radius \(R\, \text{cm},\) and is inscribed in a square. The smaller circle has center \(C,\) radius \(r \,\text{cm},\) 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 \(\dfrac{R}{r}?\)

A. \(\dfrac2{\sqrt2+1}\)

B. \(\dfrac2{\sqrt2-1}\)

C. \(\dfrac2{2\sqrt2+1}\)

D. \(\dfrac{\sqrt2+1}{\sqrt2-1}\)

E. \(\dfrac{2\sqrt2+1}{2\sqrt2-1}\)

Answer: D

Source: Official Guide