The radius of a circles is `13`cm and the length of one of its chords is `10`cm. Find the distance of the chord from the centre.

Options

A. `9 cm`
B. `10 cm`
C. `11 cm`
D. `12 cm`

Explanation

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 13 cm and a chord of length 10 cm. We need to find the distance from the center of the circle to the chord.

### Step 2: Draw the Diagram
Draw a circle with center O and a chord AB of length 10 cm. Let M be the midpoint of the chord AB. Draw a perpendicular line from the center O to the chord AB, meeting it at point M.

### Step 3: Identify the Right Triangle
Since OM is perpendicular to AB, triangle OMA is a right triangle. Here:
- OA is the radius of the circle = 13 cm
- AM (half of chord AB) = 10 cm / 2 = 5 cm
- OM is the distance we want to find.

### Step 4: Apply the Pythagorean Theorem
In the right triangle OMA, we can apply the Pythagorean theorem:
\[ OA^2 = OM^2 + AM^2 \]
Substituting the known values:
\[ 13^2 = OM^2 + 5^2 \]
This simplifies to:
\[ 169 = OM^2 + 25 \]

### Step 5: Solve for OM
Now, isolate OM^2:
\[ OM^2 = 169 - 25 \]
\[ OM^2 = 144 \]
Taking the square root:
\[ OM = \sqrt{144} = 12 \text{ cm} \]

### Conclusion
The distance of the chord from the center of the circle is **12 cm**.

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