The distance between the centres of equal circles each of radius 3 cm is 10 cm. The length of a transversal tangent is :

Options

A. 4 cm
B. 6 cm
C. 8 cm
D. 10 cm

Answer

To find the length of the transversal tangent between two equal circles, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Radius of each circle (r1 = r2) = 3 cm
- Distance between the centers of the circles (d) = 10 cm

2. **Use the Formula for the Length of the Transversal Tangent:**
The formula for the length of the transversal tangent (T) between two circles is given by:
\[ T = \sqrt{d^2 - (r_1 + r_2)^2} \]
Here, \( r_1 \) and \( r_2 \) are the radii of the two circles.

3. **Substitute the Values into the Formula:**
Since both circles have the same radius:
\[ r_1 + r_2 = 3 + 3 = 6 \text{ cm} \]
Now substitute the values into the formula:
\[ T = \sqrt{10^2 - 6^2} \]

4. **Calculate the Squares:**
- \( 10^2 = 100 \)
- \( 6^2 = 36 \)

5. **Subtract the Squares:**
\[ T = \sqrt{100 - 36} = \sqrt{64} \]

6. **Find the Square Root:**
\[ T = 8 \text{ cm} \]

### Final Answer:
The length of the transversal tangent is **8 cm**.

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