In a circle of radius 10 cm, a chord is at a distance of 6 cm from the centre. The length of chord is

Options

A. 16 cm
B. 12 cm
C. 14 cm
D. 20 cm

Answer

To find the length of the chord in a circle with a radius of 10 cm, where the chord is at a distance of 6 cm from the center, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Radius of the circle (OA) = 10 cm
- Distance from the center to the chord (OM) = 6 cm

2. **Draw the Diagram**:
- Draw a circle with center O.
- Draw a chord AB.
- Draw a perpendicular line from the center O to the chord AB, meeting it at point M.

3. **Apply the Pythagorean Theorem**:
- In the right triangle OAM, we can apply the Pythagorean theorem.
- According to the theorem:
\[ OA^2 = OM^2 + AM^2 \]
- Here, OA is the radius, OM is the distance from the center to the chord, and AM is half the length of the chord.

4. **Substitute the Known Values**:
- Substitute OA = 10 cm and OM = 6 cm into the equation:
\[ 10^2 = 6^2 + AM^2 \]
- This simplifies to:
\[ 100 = 36 + AM^2 \]

5. **Solve for AM**:
- Rearranging the equation gives:
\[ AM^2 = 100 - 36 \]
\[ AM^2 = 64 \]
- Taking the square root of both sides:
\[ AM = \sqrt{64} = 8 \text{ cm} \]

6. **Calculate the Length of the Chord**:
- Since AM is half the length of the chord AB, the full length of the chord is:
\[ AB = 2 \times AM = 2 \times 8 = 16 \text{ cm} \]

### Final Answer:
The length of the chord is **16 cm**.

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