A chord of length 60 cm is at a distance of 16 cm from the centre of a circle . What is the radius (in cm ) of the circle ?

Options

A. 17
B. 34
C. 51
D. 68

Answer

To find the radius of the circle given a chord of length 60 cm that is 16 cm away from the center, we can use the Pythagorean theorem. Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Understand the Geometry**:
- We have a circle with a chord AB of length 60 cm.
- The distance from the center of the circle (O) to the chord (AB) is 16 cm.

2. **Identify the Midpoint of the Chord**:
- Let M be the midpoint of the chord AB. Since the chord is 60 cm long, AM = MB = 30 cm.

3. **Draw the Right Triangle**:
- Draw the radius OA from the center O to the midpoint M of the chord.
- This forms a right triangle OMA, where:
- OM = 16 cm (the distance from the center to the chord)
- AM = 30 cm (half the length of the chord)
- OA = R (the radius we want to find)

4. **Apply the Pythagorean Theorem**:
- According to the Pythagorean theorem:
\[ OA^2 = OM^2 + AM^2 \]
- Substituting the values:
\[ R^2 = 16^2 + 30^2 \]

5. **Calculate the Squares**:
- Calculate \(16^2\):
\[ 16^2 = 256 \]
- Calculate \(30^2\):
\[ 30^2 = 900 \]

6. **Add the Squares**:
- Now, add these two values:
\[ R^2 = 256 + 900 = 1156 \]

7. **Find the Radius**:
- Take the square root of both sides to find R:
\[ R = \sqrt{1156} = 34 \text{ cm} \]

### Final Answer:
The radius of the circle is **34 cm**.

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