Two circles touch each other externally. The distance between their centres is 7 cm. If the radius of one circle is 4 cm, then the radius of the other circle is

Options

A. 3.5 cm
B. 3 cm
C. 4 cm
D. 2 cm

Answer

To solve the problem of finding the radius of the second circle when two circles touch each other externally, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We have two circles that touch each other externally. The distance between their centers is given as 7 cm. The radius of one circle (let's call it Circle 1) is given as 4 cm. We need to find the radius of the second circle (let's call it Circle 2).

2. **Identify the Variables**:
- Let the radius of Circle 1 (R1) = 4 cm.
- Let the radius of Circle 2 (R2) be what we need to find.
- The distance between the centers of the two circles (D) = 7 cm.

3. **Use the Relationship of Distances**: When two circles touch each other externally, the distance between their centers is equal to the sum of their radii. This can be expressed mathematically as:
\[ D = R1 + R2 \]

4. **Substitute the Known Values**: We can substitute the known values into the equation:
\[ 7 = 4 + R2 \]

5. **Solve for R2**: To find the radius of Circle 2, we can rearrange the equation:
\[ R2 = 7 - 4 \]
\[ R2 = 3 \text{ cm} \]

6. **Conclusion**: The radius of the second circle is 3 cm.

### Final Answer:
The radius of the other circle is **3 cm**.