A _____ is a simple closed curve, all of whose points are at the same distance from a fixed point.

Options

A. Diameter
B. Radius
C. Triangle
D. Circle

Answer

**Step-by-Step Solution:**

1. **Understanding the Definition**: We need to identify a simple closed curve where all points are equidistant from a fixed point.

2. **Identifying Key Terms**:
- A **simple closed curve** is a curve that starts and ends at the same point without crossing itself.
- The **fixed point** is the center of the curve.
- The **distance** from the fixed point to any point on the curve is constant and is known as the radius.

3. **Visualizing the Curve**: Imagine a point in the center (the fixed point) and draw a curve around it such that every point on the curve is the same distance from this center point.

4. **Recognizing the Shape**: The only shape that fits this description is a circle. A circle is defined as the set of all points in a plane that are a fixed distance (the radius) from a central point.

5. **Final Answer**: Therefore, the answer to the question is that the shape described is called a **circle**.

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