Question

In the given figure, $\angle ABC=45°$, then

• A. $OA<OC$
• B. $OA\perp AB$
• C. $OA=AB$
• D. $OA\perp OC$

Answer 1

The correct option is D

$OA\perp OC$

Explantion for correct statement

From the diagram given in the question,

We have, $\angle ABC=45°$

As we know,

Using property of circle.

The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

So, from above,

$$\begin{gathered} \angle AOC=2\times \angle ABC \\ \Rightarrow \angle AOC=2\times 45°=90° \end{gathered}$$

As $\angle AOC=90°$, it means the lines $AO$ and $AC$are perpendicular to each other.

Hence, $OA\perp OC$

Hence, option (D) is the correct answer.