The locus of a point at a distance 3 cm from a fixed point.

Answer

To solve the problem of finding the locus of a point that is always at a distance of 3 cm from a fixed point, we can follow these steps:

### Step-by-step Solution:

1. **Identify the Fixed Point**:
Let's denote the fixed point as \( O \). This point will serve as the center of our locus.

2. **Define the Distance**:
The problem states that the point \( P \) is always at a distance of 3 cm from the fixed point \( O \).

3. **Understanding the Locus**:
The locus of a point is the set of all positions that the point can occupy while maintaining the specified distance from the fixed point. In this case, as point \( P \) moves around point \( O \), it maintains a constant distance of 3 cm.

4. **Visualizing the Locus**:
As point \( P \) moves around point \( O \) while keeping the distance of 3 cm, it traces out a shape. This shape is a circle.

5. **Determine the Circle's Properties**:
- The center of the circle is the fixed point \( O \).
- The radius of the circle is the distance from \( O \) to \( P \), which is 3 cm.

6. **Conclusion**:
Therefore, the locus of the point \( P \) at a distance of 3 cm from the fixed point \( O \) is the circumference of a circle with a radius of 3 cm and center at point \( O \).

### Final Answer:
The locus of a point at a distance of 3 cm from a fixed point is the circumference of a circle with a radius of 3 cm, centered at the fixed point.

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