Question

If the chords $\text{AB}$ and $\text{CD}$ are of the same length, then

• A. $\text{OM}$ and $\text{ON}$ are of same length
• B. $\text{OM}$ and $\text{ON}$ are of different length
• C. Cannot say about length of $\text{OM}$ and $\text{ON}$
• D. None of the above

Answer 1

The correct option is A $\text{OM}$ and $\text{ON}$ are of same length

Here,
$\text{OM}$ $=$ Distance of chord $\text{AB}$ from center $\text{O}$
$\text{ON}$ $=$ Distance of chord $\text{CD}$ from center $\text{O}$

Given that,
Length of chord $\text{AB}$ $=$ Length of chord $\text{CD}$

Note: If two chords are of the same length, then their distances from the center will be the same.
So,
Length of $\text{OM}$ $=$ Length of $\text{ON}$

Thus, $\text{OM}$ and $\text{ON}$ will be at the same distances from the chord $\text{AB}$ and $\text{CD}$ respectively.