Calculate the length of the tangent (in cm) which is drawn from a point at a distance of 13 cm from the centre and the largest chord of that circle is 10 cm.

Options

A. 10
B. 12
C. 15
D. 16

Answer

To calculate the length of the tangent drawn from a point outside the circle, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Diameter and Radius of the Circle:**
- The largest chord of the circle is given as 10 cm. Since the largest chord is the diameter, we can determine the radius.
- Diameter (D) = 10 cm
- Radius (R) = D/2 = 10 cm / 2 = 5 cm

2. **Identify the Distance from the Center to the Point:**
- The distance from the center of the circle to the point from which the tangent is drawn is given as 13 cm.

3. **Use the Pythagorean Theorem:**
- When a tangent is drawn from a point outside the circle, it forms a right triangle with the radius and the line connecting the center of the circle to the point.
- In this triangle:
- The hypotenuse (distance from the center to the point) = 13 cm
- One leg (radius of the circle) = 5 cm
- The other leg (length of the tangent) = AB (which we need to find)

4. **Apply the Pythagorean Theorem:**
- According to the Pythagorean theorem:
\[ (hypotenuse)^2 = (radius)^2 + (tangent)^2 \]
- Plugging in the values:
\[ 13^2 = 5^2 + AB^2 \]
- This simplifies to:
\[ 169 = 25 + AB^2 \]

5. **Solve for AB:**
- Rearranging the equation gives:
\[ AB^2 = 169 - 25 \]
\[ AB^2 = 144 \]
- Taking the square root of both sides:
\[ AB = \sqrt{144} = 12 \text{ cm} \]

### Final Answer:
The length of the tangent is **12 cm**.