r : Two chords of a circle subtend equal angles at centre if and only if they are equal.
Statement r can be interpreted as

Options

A. Two chords of a circle subtend equal angle at the centre if they are equal
B. Two chords of a circle are equal if they subtend equal angle at the centre
C. Both (1) & (2)
D. None of these

Answer

To solve the problem, we need to interpret the statement \( r \): "Two chords of a circle subtend equal angles at the center if and only if they are equal."

### Step-by-Step Solution:

1. **Understanding the Statement**:
The statement \( r \) can be broken down into two parts:
- If two chords subtend equal angles at the center, then they are equal.
- If two chords are equal, then they subtend equal angles at the center.

2. **Identifying the Necessary and Sufficient Conditions**:
- The phrase "if and only if" indicates a biconditional relationship, meaning both conditions must hold true simultaneously.
- The first part of the statement establishes a necessary condition: equal angles imply equal chords.
- The second part establishes a sufficient condition: equal chords imply equal angles.

3. **Interpreting the Statement**:
We need to find interpretations of statement \( r \) that maintain its meaning:
- **Option 1**: "Two chords of a circle subtend equal angles at the center if they are equal."
- This is a necessary condition derived from the original statement, meaning if the chords are equal, they must subtend equal angles. This is consistent with the original statement.
- **Option 2**: "Two chords of a circle are equal if they subtend equal angles at the center."
- This is the converse of the original statement. It states that if the angles are equal, then the chords must be equal. This also holds true based on the original statement.
- **Option 3**: "Both 1 and 2."
- Since both options 1 and 2 are valid interpretations of statement \( r \), this option is also correct.

4. **Conclusion**:
The correct interpretation of statement \( r \) is captured by option 3, which includes both interpretations from options 1 and 2.

### Final Answer:
The interpretation of statement \( r \) is option 3: "Both 1 and 2."