Question

In the given figure, if 2AO = OC, then the ratio of area of AOB to COD is

• A. 4 : 3
• B. 1 : 4
• C. 1 : 2
• D. 2 : 3

Answer 1

The correct option is B 1 : 4

Given: 2AO = OC

In $\Delta AOB$ and $\Delta COD$,
$\angle BAO=\angle DCO$ (Each ${90}^0$)
$\angle AOB=\angle DOC$ (Vertically opposite angles)
$\therefore \Delta AOB\sim \Delta COD$ (AA similarity)
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Thus, $\frac{AreaofDAOB}{AreaofDCOD}=\frac{AO}{2AO}$
$\frac{AreaofDAOB}{AreaofDCOD}=\frac{1}{4}$
$Rightarrow$ Area of DAOB : Area of DCOD = 1 : 4
Hence, the correct answer is option (2).