If the given figure, E and F are the centers of two identical circles. What is the ratio of area of triangle AOB to the area of triangle DOC?

If the given figure, E and F are the centers of two identical circles. What is the ratio of area of triangle AOB to the area of triangle DOC?

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& \Delta DEM\sim \Delta DBN\\ & \therefore \frac{EM}{BN}=\frac{DM}{DN}\\ & \frac{r}{2r}=\frac{DM}{DN}\\ & \Rightarrow DM:MN=1:1\\ & \text{Similarly }MN:NC=1:1\\ & \frac{\text{ar}\text{. }\Delta AOB}{\text{ar}\text{. }\Delta DOC}={\left(\frac{1}{3}\right)}^2=\frac{1}{9}=1:9\end{array}$$