Question

Three circles with radii 1 unit each touch each other externally while a bigger circle encloses all the three circles as shown in the figure. A smaller circle is drawn in the area enclosed by the three circles, concentric with the bigger circle such that it touches all the three circles. The ratio of radius of the smallest circle to that of the biggest circle is: (Figure.)

• A. $\frac{1}{4-2\sqrt{3}}$
• B. $\frac{1}{2+\sqrt{3}}$
• C. $\frac{1}{7+4\sqrt{3}}$
• D. $\frac{1}{3+\sqrt{3}}$

Answer 1

The correct option is C $\frac{1}{7+4\sqrt{3}}$

The correct answer is option (c). Check the video for the approach.