A chord of length 8 cm is drawn at a distance of 3 cm from the centre of a circle. Calculate the radius of the circle.

Answer

To solve the problem of finding the radius of a circle given a chord of length 8 cm that is 3 cm away from the center of the circle, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Components**:
- Let the center of the circle be point O.
- Let the chord be AB, where the length of AB is 8 cm.
- The distance from the center O to the chord AB is 3 cm.

2. **Find the Midpoint of the Chord**:
- Let M be the midpoint of the chord AB.
- Since AB is 8 cm long, AM = MB = AB/2 = 8 cm / 2 = 4 cm.

3. **Draw a Right Triangle**:
- Draw a line from point O to point M. This line (OM) is perpendicular to the chord AB.
- In triangle OMB, we have:
- OM = 3 cm (the distance from the center to the chord),
- MB = 4 cm (half the length of the chord),
- OB = R (the radius of the circle).

4. **Apply the Pythagorean Theorem**:
- According to the Pythagorean theorem, in triangle OMB:
\[ OB^2 = OM^2 + MB^2 \]
- Substituting the known values:
\[ R^2 = 3^2 + 4^2 \]

5. **Calculate the Squares**:
- Calculate \(3^2\) and \(4^2\):
\[ 3^2 = 9 \quad \text{and} \quad 4^2 = 16 \]
- Therefore:
\[ R^2 = 9 + 16 = 25 \]

6. **Find the Radius**:
- Take the square root of both sides to find R:
\[ R = \sqrt{25} = 5 \text{ cm} \]

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

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