Equal Chords are Equidistant from Centre

Q.
In the given figure, $O$ is the centre of circle and $AB=BC$, $OD$ and $OE$ are perpendicular to $BC$ and $AB$ respectively. $OD$ is perpendicular to $OE$ also $OD=5$ cm. Find $DE$.

1. $5$ cm
2. $5\sqrt{2}$ cm
3. $10$ cm
4. $10\sqrt{2}$ cm

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

1. $\text{OM}=\text{ON}$ and $\text{OX}=\text{OY}$
2. $\text{OM}=\text{OX}$ and $\text{ON}=\text{OY}$
3. $\text{OM}=\text{OY}$ and $\text{ON}=\text{OX}$
4. None of the above

Q. In the given figure, $OA=OB$ then which of the following is correct ?

1. $PT=ST$
2. $PR=SQ$
3. $PT+RT+PR=ST+QT+SQ$
4. $PQ=RS$

Q. When chords of equal length are equidistant from the center, do they lie on the same side of the circle's center?

1. Yes
2. No
3. May be
4. Cannot say

Q. If $\text{OM}=\text{ON}=4$ units, then

1. $\text{AB}=\text{CD}$
2. $\text{AB}\ge \text{CD}$
3. $\text{AB}\le \text{CD}$
4. None of the above

Q. From the given figure below, what are the length of the chords $\text{CD}$ and $\text{RS}$ if $\text{O'M}=\text{O'N},\text{OX}=\text{OY}$ and the length of $\text{AM}$ and $\text{PX}$ are $2$ units and $3$ units respectively.

1. $\text{CD}=4$ units
   $\text{RS}=6$ units
2. $\text{CD}=6$ units
   $\text{RS}=4$ units
3. $\text{CD}=4$ units
   $\text{RS}=9$ units
4. $\text{CD}=9$ units
   $\text{RS}=4$ units

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

1. $\text{OM}$ and $\text{ON}$ are of same length
2. $\text{OM}$ and $\text{ON}$ are of different length
3. Cannot say about length of $\text{OM}$ and $\text{ON}$
4. None of the above