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UKMT Senior Mathematical Challenge, 2016

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The diagram shows ten equal discs that lie between two concentric circles − an inner circle and an outer circle. Each disc touches two neighbouring discs and both circles. The inner circle has radius 1. What is the radius of the outer circle?

(A) $2\tan 36°$ (B) $\frac{\sin 36°}{1 - \sin 36°}$ (C) $\frac{1 + \sin 18°}{1 - \sin 18°}$ (D) $\frac{2}{\cos 18°}$ (E) $\frac{9}{5}$

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