If two circles with diameter 8cm and 6 cm touch externally, then the distance between their centres is ______.

Options

A. 2 cm
B. 7 cm
C. 10 cm
D. 14 cm

Answer

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

### Step 1: Identify the diameters of the circles
The diameters of the two circles are given as:
- Circle 1: Diameter = 8 cm
- Circle 2: Diameter = 6 cm

### Step 2: Calculate the radii of the circles
The radius of a circle is half of its diameter. Therefore, we can calculate the radii as follows:
- Radius of Circle 1 (R1) = Diameter of Circle 1 / 2 = 8 cm / 2 = 4 cm
- Radius of Circle 2 (R2) = Diameter of Circle 2 / 2 = 6 cm / 2 = 3 cm

### Step 3: Use the formula for the distance between the centers
When two circles touch externally, the distance (D) between their centers is equal to the sum of their radii:
\[ D = R1 + R2 \]

### Step 4: Substitute the values of the radii into the formula
Now we can substitute the values we calculated:
\[ D = 4 cm + 3 cm = 7 cm \]

### Step 5: Conclusion
The distance between the centers of the two circles is 7 cm.

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