A circle of radius 3 cm can be drawn through two points A, B such that AB=6 cm. State true or false

Explanation

To determine whether a circle of radius 3 cm can be drawn through two points A and B such that the distance AB is 6 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The radius of the circle (r) is given as 3 cm.
- The distance between points A and B (AB) is given as 6 cm.

2. **Identify the Relationship Between Diameter and Radius**:
- The diameter (d) of a circle is twice the radius. Therefore, we can express this relationship as:
\[ d = 2 \times r \]

3. **Calculate the Diameter Using the Given Radius**:
- Substitute the radius into the diameter formula:
\[ d = 2 \times 3 \text{ cm} = 6 \text{ cm} \]

4. **Compare the Diameter with the Length of AB**:
- We see that the calculated diameter (6 cm) is equal to the distance AB (6 cm).

5. **Conclusion**:
- Since the distance AB is equal to the diameter of the circle, it confirms that points A and B can indeed lie on a circle with a radius of 3 cm. Thus, a circle can be drawn through points A and B with the given conditions.

### Final Answer:
The statement is **True**.

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