A chord of length 16cm is drawn in a circle of radius 10cm. Find the distnace of the chord from the centre of the circle.

Answer

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

### Step 1: Understand the Geometry
We have a circle with a radius of 10 cm and a chord of length 16 cm. We need to find the perpendicular distance from the center of the circle to the chord.

### Step 2: Draw the Diagram
Draw a circle with center O and radius 10 cm. Draw the chord AB such that its length is 16 cm. Let M be the midpoint of the chord AB. Draw a line from O to M, which is the perpendicular distance we need to find.

### Step 3: Find the Length of AM
Since M is the midpoint of chord AB, we can find the length of AM:
\[ AM = \frac{AB}{2} = \frac{16 \text{ cm}}{2} = 8 \text{ cm} \]

### Step 4: Apply the Pythagorean Theorem
In the right triangle OMA, where:
- OA is the radius (10 cm),
- AM is half the chord length (8 cm),
- OM is the distance from the center to the chord (which we need to find).

According to the Pythagorean theorem:
\[ OA^2 = OM^2 + AM^2 \]
Substituting the known values:
\[ 10^2 = OM^2 + 8^2 \]
\[ 100 = OM^2 + 64 \]

### Step 5: Solve for OM
Rearranging the equation to solve for OM:
\[ OM^2 = 100 - 64 \]
\[ OM^2 = 36 \]
Taking the square root of both sides:
\[ OM = \sqrt{36} = 6 \text{ cm} \]

### Conclusion
The distance of the chord from the center of the circle is 6 cm.

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