A chord of length 8 units is at a distance of 4 uits from the centre of a circle then its radius is

Options

A. `4sqrt(2)`
B. `3sqrt(2)`
C. `2sqrt(2)`
D. `sqrt(2)`

Answer

To solve the problem, we need to find the radius of a circle given that a chord of length 8 units is at a distance of 4 units from the center of the circle.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Length of the chord (AB) = 8 units
- Distance from the center of the circle (O) to the chord (OD) = 4 units

2. **Divide the Chord:**
- The perpendicular drawn from the center of the circle to the chord bisects the chord.
- Therefore, we can find the lengths of the segments of the chord:
\[ AD = \frac{AB}{2} = \frac{8}{2} = 4 \text{ units} \]

3. **Use the Pythagorean Theorem:**
- In the right triangle OAD, we can apply the Pythagorean theorem:
\[ OA^2 = AD^2 + OD^2 \]
- Substituting the known values:
\[ OA^2 = 4^2 + 4^2 \]
\[ OA^2 = 16 + 16 = 32 \]

4. **Calculate OA:**
- Taking the square root of both sides:
\[ OA = \sqrt{32} = 4\sqrt{2} \]

5. **Conclusion:**
- The radius of the circle (OA) is \( 4\sqrt{2} \) units.

### Final Answer:
The radius of the circle is \( 4\sqrt{2} \) units.

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