Question

In the given figure, $O$ is the centre of a circle. $AB$ and $CD$ are its two chords. If $OM\perp AB$, $ON\perp CD$ and $OM=ON$, then

• A. $AB\ne CD$
• B. $AB<CD$
• C. $AB>CD$
• D. $AB=CD$

Answer 1

The correct option is D

$AB=CD$

Step 1- Comparing given data

From the given data we conclude that,

Both the chords $AB$ and $CD$ are placed at the same distance from the center of the circle $O$.

Step 2- chords equidistant from the center of a circle.

So, applying the theorem of chords equidistant from the center of a circle are equal.

We can conclude that,

The length of $AB$ will be equal to the length of $CD$.

Hence, $AB=CD$

Hence, option (D) is the correct answer.