The length of the radius of a circle with centre O is 5 cm and the length of the chord AB is 8 cm. The distance of the chord AB from the point O is

Options

A. 2 cm.
B. 3 cm.
C. 4 cm.
D. 15 cm.

Answer

To find the distance of the chord AB from the center O of the circle, we can use the following steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Radius of the circle (OA) = 5 cm
- Length of the chord (AB) = 8 cm

2. **Divide the Chord**:
- Since the line from the center O to the chord AB is perpendicular to the chord, it bisects the chord.
- Let P be the midpoint of the chord AB. Therefore, AP = PB = 8 cm / 2 = 4 cm.

3. **Create a Right Triangle**:
- Now, we can form a right triangle OAP, where:
- OA = radius = 5 cm (hypotenuse)
- AP = half of the chord = 4 cm (one leg)
- OP = distance from the center O to the chord AB (the other leg, which we need to find).

4. **Apply the Pythagorean Theorem**:
- According to the Pythagorean theorem:
\[ OA^2 = AP^2 + OP^2 \]
- Plugging in the values we have:
\[ 5^2 = 4^2 + OP^2 \]
\[ 25 = 16 + OP^2 \]

5. **Solve for OP**:
- Rearranging the equation gives:
\[ OP^2 = 25 - 16 \]
\[ OP^2 = 9 \]
- Taking the square root of both sides:
\[ OP = \sqrt{9} = 3 \text{ cm} \]

### Conclusion:
The distance of the chord AB from the point O is **3 cm**.