The length of the chord of a circle is 8 cm and perpendicular distance between centre and the chord is 3 cm. Then the radius of the circle is equal to :

Options

A. 4 cm
B. 5 cm
C. 6 cm
D. 8 cm

Answer

To find the radius of the circle given the length of the chord and the perpendicular distance from the center to the chord, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Length of the chord (AB) = 8 cm
- Perpendicular distance from the center (O) to the chord (AB) = 3 cm

2. **Divide the Chord**:
- Since the perpendicular from the center to the chord bisects the chord, we can find the half-length of the chord.
- Half of the chord (AM) = AB/2 = 8 cm / 2 = 4 cm

3. **Form a Right Triangle**:
- We can form a right triangle using the radius (r), half of the chord (AM), and the perpendicular distance (OM).
- In triangle OMA:
- OM = 3 cm (perpendicular distance)
- AM = 4 cm (half of the chord)
- OA = r (radius of the circle)

4. **Apply the Pythagorean Theorem**:
- According to the Pythagorean theorem:
\[ OA^2 = OM^2 + AM^2 \]
- Plugging in the values:
\[ r^2 = 3^2 + 4^2 \]
\[ r^2 = 9 + 16 \]
\[ r^2 = 25 \]

5. **Calculate the Radius**:
- Taking the square root of both sides:
\[ r = \sqrt{25} = 5 \text{ cm} \]

### Final Answer:
The radius of the circle is **5 cm**.