The shape of the set of all points in a plane equidistant from a certain point is a circle. This concept is known as a circle in geometry. A circle is defined as the set of all points that are a fixed distance, known as the radius, from a central point. The distance between any point on the circle and the center is always the same, making it a symmetrical and uniform shape.

Circles have many unique properties that make them important in various fields such as mathematics, engineering, and design. They are known for their symmetry, which allows them to be easily identified and studied. Circles also play a crucial role in trigonometry, where they are used to define important functions such as sine and cosine.

In addition to their mathematical significance, circles are also commonly used in everyday life. They can be found in objects such as wheels, clocks, and coins. The shape of a circle is aesthetically pleasing and is often used in art and design to create visually appealing compositions.

To learn more about circles and their properties, you can visit websites such as Math is Fun or Khan Academy. These resources provide detailed explanations and examples to help you better understand the concept of circles and their applications.

Overall, the shape of the set of all points in a plane equidistant from a certain point is a circle. Circles are versatile shapes that have both practical and theoretical significance. By studying circles, we can gain a deeper understanding of geometry and its applications in various fields.

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