Circle – Introduction

A circle is a shape with all points at the same distance from its center. This distance is called the radius. Let’s break this down with diagrams and examples:

Definition of a Circle

• Circle: A set of all points in a plane that are equidistant from a fixed point, called the center.

Key Components

1. Center: The fixed point from which all points on the circle are equidistant.
2. Radius (r): The distance from the center to any point on the circle.
3. Diameter (d): The distance across the circle, passing through the center. It is twice the length of the radius (d = 2r).
4. Circumference: The distance around the circle.

• O is the center.
• OA is the radius.

Examples

Example 1: Finding the Radius

Suppose we have a circle with a diameter of 10 cm.

To find the radius: r=d/2​=10/2 cm​ =5 cm

Example 2: Drawing a Circle

To draw a circle with a radius of 3 cm:

1. Place the compass point on a paper where we want the center.
2. Adjust the compass to open 3 cm wide.
3. Rotate the compass 360 degrees to draw the circle.

Real-life Examples

• Wheels: The rim of a wheel forms a circle, with the axle as the center.
• Clocks: The face of a round clock is a circle, with the center being where the hands rotate.
• Pizza: A round pizza is an example of a circle, with each slice’s tip meeting at the center.

Understanding Through Activity

• Activity: Use a string and a thumbtack to draw a circle. Fix the thumbtack at the center, tie the string to the thumbtack, stretch the string, and use a pencil to trace the circle by keeping the string taut.

By understanding these components and practicing with diagrams and examples, we can easily grasp the concept of a circle.