Question

In the given figure, if $OA\times OB=OC\times OD$, then find the value of $\angle C$.

• A. ${30}^{\circ }$
• B. ${20}^{\circ }$
• C. ${40}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C ${40}^{\circ }$

The given figure is,

$OA\times OB=OC\times OD$

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

Also, $\angle AOD=\angle COB$ . . . (ii) (Vertically opposite angles)

From equation (i) and (ii),
$△AOD$ is similar to $△COB$ (Side - Angle - Side Theorem)

Therefore, $\angle A=\angle C$ (Corresponding angles of similar triangles)

$\angle A={40}^{\circ }$ (Given)

Therefore, $\angle C={40}^{\circ }$