If the radius of the circumcircle of an equilateral triangle is 8cm then the measure of radius of its incircle is:

Options

A. 8cm
B. 4cm
C. 16cm
D. 12cm

Answer

To find the radius of the incircle of an equilateral triangle given the radius of its circumcircle, we can use the relationship between the two radii.

### Step-by-Step Solution:

1. **Understand the relationship between circumradius (R) and inradius (r)**:
For an equilateral triangle, the radius of the circumcircle (R) is related to the radius of the incircle (r) by the formula:
\[ R = 2r \]

2. **Given data**:
We are given that the radius of the circumcircle (R) is 8 cm.

3. **Set up the equation**:
Using the relationship from step 1, we can substitute the value of R:
\[ 8 = 2r \]

4. **Solve for the inradius (r)**:
To find r, divide both sides of the equation by 2:
\[ r = \frac{8}{2} = 4 \text{ cm} \]

5. **Conclusion**:
The radius of the incircle of the equilateral triangle is 4 cm.

### Final Answer:
The radius of the incircle is **4 cm**.

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