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?

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?

Answer: Option B

Solution

Answer: Option B

Solution:

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

$$\begin{array}{rl}& \frac{\text{OC}}{{\text{O}}_1\text{C}}=\frac{\text{OD}}{{\text{O}}_1\text{E}}\\ & \frac{4}{\text{R}+2+4}=\frac{2}{\text{R}}\end{array}$$
4R = 2R + 12
2R = 12
R = 6