From the centre of a circle, distance of a chord is 16 cm. If radius of the circle be 20 cm. What will be the length of the chord?

Options

A. 6 cm
B. 12 cm
C. 24 cm
D. 36 cm

Answer

To find the length of the chord in the circle, we can follow these steps:

### Step 1: Understand the Problem
We have a circle with a radius of 20 cm and a chord that is 16 cm away from the center of the circle. We need to find the length of the chord.

### Step 2: Draw the Diagram
Draw a circle and label the center as O. Let the chord be AB. Draw a perpendicular line from O to the chord AB, meeting it at point K. This line represents the distance from the center to the chord, which is given as 16 cm.

### Step 3: Identify the Right Triangle
In triangle OAK (where A is one endpoint of the chord and K is the midpoint of the chord), we have:
- OA = radius of the circle = 20 cm
- OK = distance from the center to the chord = 16 cm
- AK = half the length of the chord (which we will find)

### Step 4: Apply the Pythagorean Theorem
Since triangle OAK is a right triangle, we can use the Pythagorean theorem:
\[ OA^2 = OK^2 + AK^2 \]

Substituting the known values:
\[ 20^2 = 16^2 + AK^2 \]

### Step 5: Calculate the Squares
Calculate the squares:
\[ 400 = 256 + AK^2 \]

### Step 6: Solve for AK^2
Rearranging the equation gives:
\[ AK^2 = 400 - 256 \]
\[ AK^2 = 144 \]

### Step 7: Find AK
Taking the square root of both sides:
\[ AK = \sqrt{144} = 12 \text{ cm} \]

### Step 8: Find the Length of the Chord
Since AK is half the length of the chord AB:
\[ AB = 2 \times AK = 2 \times 12 = 24 \text{ cm} \]

### Final Answer
The length of the chord AB is **24 cm**.

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