In a circle of radius 25 cm, a chord is drawn at a distance of 7 cm from the centre. Find the length of the chord.

Options

A. 24 cm
B. 48 cm
C. 50 cm
D. 36 cm

Answer

To solve the problem of finding the length of a chord in a circle, we can follow these steps:

### Step 1: Understand the given information
We have a circle with:
- Radius (r) = 25 cm
- Distance from the center to the chord (d) = 7 cm

### Step 2: Visualize the problem
Draw a circle and label the center as O. Draw a chord AB such that the perpendicular distance from O to the chord AB is OC, where OC = 7 cm. The radius OA = 25 cm.

### Step 3: Form a right triangle
In triangle OAC:
- OA is the hypotenuse (radius) = 25 cm
- OC is one leg (distance from the center to the chord) = 7 cm
- AC is the other leg (half the length of the chord)

### Step 4: Apply the Pythagorean theorem
According to the Pythagorean theorem:
\[ OA^2 = OC^2 + AC^2 \]

Substituting the known values:
\[ 25^2 = 7^2 + AC^2 \]

### Step 5: Calculate the squares
Calculating the squares:
- \( 25^2 = 625 \)
- \( 7^2 = 49 \)

So, we have:
\[ 625 = 49 + AC^2 \]

### Step 6: Rearrange the equation
Rearranging gives:
\[ AC^2 = 625 - 49 \]
\[ AC^2 = 576 \]

### Step 7: Find AC
Taking the square root of both sides:
\[ AC = \sqrt{576} = 24 \text{ cm} \]

### Step 8: Find the length of the chord AB
Since AC is half of the chord AB, we can find the full length of the chord:
\[ AB = 2 \times AC = 2 \times 24 = 48 \text{ cm} \]

### Final Answer
The length of the chord AB is **48 cm**.

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