In the given figure, ABC is a right-angled triangle. ∠ABC = 90° and ∠ACB = 60°. If the radius of the smaller circle is 2 cm, then what is the radius (in cm) of the larger circle?

Solution (By Examveda Team)

OCD = 30°
OD = 2
OC = 4
O₁E = R
O₁O = R + 2
ΔOCD Similar to ΔO₁CE

$$\eqalign{ & \frac{{{\text{OC}}}}{{{{\text{O}}_1}{\text{C}}}} = \frac{{{\text{OD}}}}{{{{\text{O}}_1}{\text{E}}}} \cr & \frac{4}{{{\text{R}} + 2 + 4}} = \frac{2}{{\text{R}}} \cr} $$
4R = 2R + 12
2R = 12
R = 6