The radius of a circle is 13 cm and the length of one of its chords is 24 cm. Find the distance of the chord from the centres.

Answer

To find the distance of the chord from the center of the circle, we can follow these steps:

### Step-by-Step Solution:

1. **Draw the Circle and Label the Points**:
- Draw a circle with center \( O \) and a chord \( AB \). Mark the midpoint of the chord \( AB \) as \( M \).

2. **Identify Given Values**:
- The radius of the circle \( r = 13 \) cm.
- The length of the chord \( AB = 24 \) cm.

3. **Calculate Half the Length of the Chord**:
- Since \( M \) is the midpoint of chord \( AB \), we have:
\[ AM = MB = \frac{AB}{2} = \frac{24}{2} = 12 \text{ cm} \]

4. **Set Up the Right Triangle**:
- In triangle \( OMB \), \( OM \) is the distance from the center \( O \) to the chord \( AB \) (which we will denote as \( x \)), and \( MB = 12 \) cm. The radius \( OB = 13 \) cm.

5. **Apply the Pythagorean Theorem**:
- According to the Pythagorean theorem:
\[ OB^2 = OM^2 + MB^2 \]
- Substituting the known values:
\[ 13^2 = x^2 + 12^2 \]

6. **Calculate the Squares**:
- Calculate \( 13^2 \) and \( 12^2 \):
\[ 169 = x^2 + 144 \]

7. **Solve for \( x^2 \)**:
- Rearranging the equation gives:
\[ x^2 = 169 - 144 \]
\[ x^2 = 25 \]

8. **Find \( x \)**:
- Taking the square root of both sides:
\[ x = \sqrt{25} = 5 \text{ cm} \]

9. **Conclusion**:
- The distance of the chord from the center of the circle is \( 5 \) cm.

### Final Answer:
The distance of the chord from the center of the circle is **5 cm**.