Two circles of radius 5 cm and 4 cm touch each other. Find the distance between their centers.

Answer

To solve the problem of finding the distance between the centers of two circles that touch each other, we will follow these steps:

### Step 1: Understand the Problem
We have two circles with given radii:
- Radius of the first circle (R1) = 5 cm
- Radius of the second circle (R2) = 4 cm

The circles are touching each other. We need to determine the distance between their centers.

### Step 2: Identify the Type of Touching
Since the problem states that the circles touch each other, we need to consider two scenarios:
1. **Externally touching circles**: The distance between their centers is the sum of their radii.
2. **Internally touching circles**: The distance between their centers is the difference of their radii.

### Step 3: Calculate the Distance for Externally Touching Circles
If the circles are touching each other externally, the formula for the distance \( D \) between their centers is:
\[ D = R1 + R2 \]

Substituting the values:
\[ D = 5 \, \text{cm} + 4 \, \text{cm} = 9 \, \text{cm} \]

### Step 4: Calculate the Distance for Internally Touching Circles
If the circles are touching each other internally, the formula for the distance \( D \) between their centers is:
\[ D = R1 - R2 \]

Substituting the values:
\[ D = 5 \, \text{cm} - 4 \, \text{cm} = 1 \, \text{cm} \]

### Conclusion
The distance between the centers of the two circles depends on how they are touching:
- If they are touching externally, the distance is **9 cm**.
- If they are touching internally, the distance is **1 cm**.