A chord of length 30 cm is at a distance of 8 cm from the centre of a circle. The radius of the circle is :

Options

A. 17 cm
B. 23 cm
C. 21 cm
D. 19 cm

Answer

To find the radius of the circle given a chord of length 30 cm that is 8 cm away from the center, 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, with a length of 30 cm.
- The distance from the center O to the chord AB is 8 cm. We will denote this distance as OP, where P is the midpoint of the chord AB.

2. **Divide the Chord**:
- Since P is the midpoint of chord AB, we can divide the chord into two equal segments. Therefore, AP = PB = 30 cm / 2 = 15 cm.

3. **Draw a Right Triangle**:
- Now, we can form a right triangle OAP, where:
- OP = 8 cm (the distance from the center to the chord),
- AP = 15 cm (half the length of the chord),
- OA = R (the radius of the circle, which we need to find).

4. **Apply the Pythagorean Theorem**:
- According to the Pythagorean theorem, in triangle OAP:
\[ OA^2 = OP^2 + AP^2 \]
- Substituting the known values:
\[ R^2 = 8^2 + 15^2 \]
\[ R^2 = 64 + 225 \]
\[ R^2 = 289 \]

5. **Calculate the Radius**:
- To find R, we take the square root of both sides:
\[ R = \sqrt{289} = 17 \text{ cm} \]

### Final Answer:
The radius of the circle is **17 cm**.

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