Question

If $\text{AB}=\text{CD}$ and $\text{PQ}=\text{RS}$, then

• A. $\text{OM}=\text{ON}$ and $\text{OX}=\text{OY}$
• B. $\text{OM}=\text{OX}$ and $\text{ON}=\text{OY}$
• C. $\text{OM}=\text{OY}$ and $\text{ON}=\text{OX}$
• D. None of the above

Answer 1

The correct option is A $\text{OM}=\text{ON}$ and $\text{OX}=\text{OY}$

Here,
$\text{OM}$ and $\text{ON}$ are the distances from the center 'O' for the chords $\text{AB}$ and $\text{CD}$ respectively.
$\text{OX}$ and $\text{OY}$ are the distances from the center for the chords $\text{PQ}$ and $\text{RS}$ respectively.

Note: Chords of a circle that are equal in length are equidistant from the center.

Thus, $\text{AB}=\text{CD}$ and $\text{PQ}=\text{RS}$