The length of a chord of a circle of radius 10 cm is 12 cm. Find the distance of the chord from the centre of the circle.

Options

A. 6 cm
B. 5 cm
C. 8 cm
D. 7 cm

Answer

To find the distance of the chord from the center of the circle, we can follow these steps:

### Step-by-Step Solution:

1. **Draw the Circle and Label Points**:
- Draw a circle with a radius of 10 cm. Label the center of the circle as point O.
- Draw a chord AB of length 12 cm.

2. **Identify the Midpoint**:
- Since the chord AB is 12 cm long, its midpoint M can be found. The length of AM and MB will each be half of AB.
- Therefore, AM = MB = 12 cm / 2 = 6 cm.

3. **Draw a Perpendicular from the Center**:
- Draw a perpendicular line from point O (the center) to the chord AB, which will intersect the chord at point M.

4. **Apply the Pythagorean Theorem**:
- In the right triangle OMA, we can apply the Pythagorean theorem.
- The hypotenuse OA (which is the radius) is 10 cm, and one leg AM is 6 cm. We need to find the other leg OM (the distance from the center to the chord).

5. **Set Up the Equation**:
- According to the Pythagorean theorem:
\[ OA^2 = OM^2 + AM^2 \]
- Substituting the known values:
\[ 10^2 = OM^2 + 6^2 \]
- This simplifies to:
\[ 100 = OM^2 + 36 \]

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

7. **Conclusion**:
- The distance of the chord from the center of the circle is 8 cm.