Describe the locus of points at distances less than 3 cm from a given point.

Answer

To describe the locus of points that are at a distance less than 3 cm from a given point, follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Point**: Let's denote the given point as \( O \). This point will serve as the center for our locus description.

2. **Draw a Circle**: Using a compass, draw a circle with a radius of 3 cm centered at point \( O \). This circle represents all points that are exactly 3 cm away from point \( O \).

3. **Understand the Locus Requirement**: The problem states that we are looking for points that are at a distance less than 3 cm from point \( O \). This means we are interested in the area inside the circle, not on the circumference.

4. **Describe the Locus**: The locus of points at a distance less than 3 cm from point \( O \) is the interior of the circle. In mathematical terms, this can be described as all points \( P \) such that the distance \( OP < 3 \) cm.

5. **Final Conclusion**: Therefore, the locus of points at a distance less than 3 cm from the given point \( O \) is the area inside the circle with radius 3 cm centered at point \( O \).