If the lengths of the tangents from two points A, B to a circle are 4, 3 respectively. If A,B are conjugate points then AB=

Options

A. 5
B. `sqrt(85)`
C. `(sqrt(85))/2`
D. `(sqrt(85))/3`

Answer

To solve the problem, we need to find the distance \( AB \) between two conjugate points \( A \) and \( B \) from which tangents of lengths \( L_1 \) and \( L_2 \) are drawn to a circle. The lengths of the tangents are given as follows:

- Length of tangent from point \( A \) (denoted as \( L_1 \)) = 4
- Length of tangent from point \( B \) (denoted as \( L_2 \)) = 3

### Step-by-Step Solution:

1. **Identify the lengths of the tangents**:
- We have \( L_1 = 4 \) and \( L_2 = 3 \).

2. **Use the formula for the distance between conjugate points**:
- The distance \( AB \) between the conjugate points \( A \) and \( B \) can be calculated using the formula:
\[ AB = \sqrt{L_1^2 + L_2^2} \]

3. **Substitute the values of \( L_1 \) and \( L_2 \)**:
- Substitute \( L_1 = 4 \) and \( L_2 = 3 \) into the formula:
\[ AB = \sqrt{4^2 + 3^2} \]

4. **Calculate \( 4^2 \) and \( 3^2 \)**:
- Calculate \( 4^2 = 16 \) and \( 3^2 = 9 \).

5. **Add the squares**:
- Now, add the results:
\[ 16 + 9 = 25 \]

6. **Take the square root**:
- Finally, take the square root of 25:
\[ AB = \sqrt{25} = 5 \]

7. **Conclusion**:
- Therefore, the length \( AB \) is equal to 5 units.

### Final Answer:
\[ AB = 5 \]