In a circle with radius 13 cm, the length of a chord is 24 cm. Then, the distance of the chord from the centre is ......... cm.

Options

A. 10
B. 5
C. 12
D. 6.5

Answer

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

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Radius of the circle (r) = 13 cm
- Length of the chord (AB) = 24 cm

2. **Find the Midpoint of the Chord:**
- Let D be the midpoint of the chord AB. Since D is the midpoint, we have:
\[ AD = DB = \frac{AB}{2} = \frac{24 \text{ cm}}{2} = 12 \text{ cm} \]

3. **Draw a Right Triangle:**
- Draw a line from the center of the circle O to the midpoint D of the chord AB. This line OD is the distance we need to find.
- The triangle OBD is a right triangle where:
- OB is the radius = 13 cm
- BD is half the length of the chord = 12 cm

4. **Apply the Pythagorean Theorem:**
- According to the Pythagorean theorem:
\[ OB^2 = OD^2 + BD^2 \]
- Substitute the known values:
\[ 13^2 = OD^2 + 12^2 \]
- This simplifies to:
\[ 169 = OD^2 + 144 \]

5. **Solve for OD:**
- Rearranging the equation gives:
\[ OD^2 = 169 - 144 \]
- Calculate:
\[ OD^2 = 25 \]
- Taking the square root:
\[ OD = \sqrt{25} = 5 \text{ cm} \]

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

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