Two circles of radii 13 cm and 5 cm touch internally each other. Find the distance between their centres:

Options

A. 18 cm
B. 12 cm
C. 9 cm
D. 8 cm

Answer

To find the distance between the centers of two circles that touch each other internally, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Radii of the Circles**:
- Let the radius of the larger circle (Circle 1) be \( R_1 = 13 \) cm.
- Let the radius of the smaller circle (Circle 2) be \( R_2 = 5 \) cm.

2. **Understand the Configuration**:
- Since the circles touch each other internally, the distance between their centers can be calculated using the formula:
\[ \text{Distance between centers} = R_1 - R_2 \]
- This is because the distance from the center of the larger circle to the point of contact is \( R_1 \) and from the center of the smaller circle to the point of contact is \( R_2 \).

3. **Substitute the Values**:
- Substitute the values of \( R_1 \) and \( R_2 \) into the formula:
\[ \text{Distance} = 13 \, \text{cm} - 5 \, \text{cm} \]

4. **Perform the Calculation**:
- Calculate the distance:
\[ \text{Distance} = 8 \, \text{cm} \]

5. **Conclusion**:
- Therefore, the distance between the centers of the two circles is \( 8 \) cm.

### Final Answer:
The distance between the centers of the two circles is **8 cm**.

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