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The figure above shows \(2\) circles. The larger circle has center \(A,\) radius \(R\, \text{cm},\) and is inscribed in

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The figure above shows \(2\) circles. The larger circle has center \(A,\) radius \(R\, \text{cm},\) and is inscribed in

by Gmat_mission » Sun Jan 23, 2022 1:42 am

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2019-09-21_1753.png
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

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