In two Concentric circles, AB and CD are two chords of the outer circle which touch the inner circle at E and F. Then :

Options

A. AB = CD
B. `AB = (1)/(2) CD`
C. `AB ne CD`
D. None of these

Answer

To solve the problem involving two concentric circles with chords AB and CD that touch the inner circle at points E and F respectively, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
- We have two concentric circles, meaning they share the same center. Let’s denote the center as O.
- Chord AB of the outer circle touches the inner circle at point E.
- Chord CD of the outer circle touches the inner circle at point F.

**Hint**: Visualize the two circles and label the center and the points where the chords touch the inner circle.

2. **Identify the Properties of Chords**:
- Since AB touches the inner circle at E, the distance from the center O to the chord AB is equal to the radius of the inner circle at point E.
- Similarly, since CD touches the inner circle at F, the distance from O to the chord CD is equal to the radius of the inner circle at point F.

**Hint**: Remember that the distance from the center to a chord is the same as the radius of the inner circle at the point of tangency.

3. **Use the Equidistance Property**:
- The distances OE (from O to E) and OF (from O to F) are equal because both points E and F lie on the inner circle.
- Therefore, the distances from the center O to the chords AB and CD are equal.

**Hint**: Think about how the radii of a circle are always equal.

4. **Conclude About the Chords**:
- Since the distances from the center O to both chords AB and CD are equal, it follows that the lengths of the chords AB and CD must also be equal.
- Thus, we can conclude that AB = CD.

**Hint**: Reflect on the relationship between the distance from the center to the chords and the lengths of the chords themselves.

### Final Conclusion:
The lengths of the chords AB and CD are equal because they are both equidistant from the center of the concentric circles.