Question

In the given figure
$OA\times OB=OC\times OD,$ then which of the following is correct.

• A. $\angle A=\angle B$
• B. $\angle A=\angle C$
• C. $\angle D=\angle C$
• D. none of these

Answer 1

The correct option is B $\angle A=\angle C$

Given $OA\times OB=OC\times OD$

Then We have

$\frac{OA}{OC}=\frac{OD}{OB}$....(1)

In $\Delta AOD$ and $\Delta COB$

$\frac{OA}{OC}=\frac{OD}{OB}$....from (1)

$\angle AOD=\angle COB[verticallyopp.\measuredangle S]$

$\therefore \Delta AOD\sim \Delta COB$( SAS)

Now, if two triangle are similar. so, corresponding angles are equal.

$\angle A=\angle C$

and $\angle D=\angle B$