Circle `O_(1) cong `Circle `O_(2)`, If radius of circle `O_(1)=6 cm ` then diameter of circle `O_(2)` is ________

Answer

To solve the problem, we need to find the diameter of circle O2 given that circle O1 is congruent to circle O2 and the radius of circle O1 is 6 cm.

### Step-by-Step Solution:

1. **Understand Congruence of Circles**:
- Two circles are said to be congruent if they have the same radius.
- Therefore, if circle O1 is congruent to circle O2, it means that the radius of circle O1 is equal to the radius of circle O2.

2. **Identify the Radius of Circle O1**:
- We are given that the radius of circle O1 (r1) is 6 cm.
- Thus, we can write:
\[ r_1 = 6 \text{ cm} \]

3. **Determine the Radius of Circle O2**:
- Since circle O1 is congruent to circle O2, we can conclude that the radius of circle O2 (r2) is also 6 cm.
- Therefore:
\[ r_2 = r_1 = 6 \text{ cm} \]

4. **Calculate the Diameter of Circle O2**:
- The diameter (d) of a circle is calculated using the formula:
\[ d = 2 \times r \]
- Substituting the radius of circle O2 into the formula:
\[ d_2 = 2 \times r_2 = 2 \times 6 \text{ cm} = 12 \text{ cm} \]

5. **Final Answer**:
- The diameter of circle O2 is:
\[ \text{Diameter of circle O2} = 12 \text{ cm} \]