The top of your desk and a chalkboard are objects which can be used to represent a plane, although they do not satisfy the definition above.Ī circle divides the plane into three parts: Intuitively, a plane may be visualized as a flat infinite sheet of paper. In the diagram to the right, Plane P contains points A, B and C.Ĭan you think of some real world objects that satisfy the definition of a plane? At this level of mathematics, that is difficult to do. Thus we have circle A.Ī plane is a flat surface that extends without end in all directions. In the circle to the right, the center is point A. A circle is the set of points that are equidistant from a special point in the plane. Let's revisit the definition of a circle. Thus, it can be stated, every diameter is a chord, but not every chord is a diameter. This is because every diameter passes through the center of a circle, but some chords do not pass through the center. A diameter satisfies the definition of a chord, however, a chord is not necessarily a diameter. It turns out that a diameter of a circle is the longest chord of that circle since it passes through the center. By cutting along chord AB, you are cutting off a segment of pizza that includes this chord. If this circle was a pizza pie, you could cut off a piece of pizza along chord AB. The circle to the right contains chord AB. In geometry, a chord is often used to describe a line segment joining two endpoints that lie on a circle. As you can see, a circle has many different radii and diameters, each passing through its center.Ī chord is a line segment that joins two points on a curve. A straight cut made from a point on the circle, continuing through its center to another point on the circle, is a diameter. A radius is formed by making a straight cut from the center to a point on the circle. Look at the pizza to the right which has been sliced into 8 equal parts through its center. We can look at a pizza pie to find real-world examples of diameter and radius. Thus, the diameter of a circle is twice as long as the radius. If you place two radii end-to-end in a circle, you would have the same length as one diameter. The radius of a circle is the distance from the center of a circle to any point on the circle. A real-world example of diameter is a 9-inch plate. The distance across a circle through the center is called the diameter. Some real world examples of a circle are a wheel, a dinner plate and (the surface of) a coin. Thus, the circle to the right is called circle A since its center is at point A. We will also examine the relationship between the circle and the plane.Ī circle is a shape with all points the same distance from its center. Let's look at the definition of a circle and its parts. Therefore, the area of the circle is 140.4 square inches.A circle is an important shape in the field of geometry.
Finally, you would divide 1,764 by 12.57 and get 140.4. Then, you would multiply 4 by π and get 12.57. For example, if the circumference is 42 inches, first you would square 42 and get 1,764. To find the area using the circumference, or the distance around the circle, use the formula area = c^2/4π, where c is the circumference. Therefore, the area of the circle is 314.16 inches squared. Then, plug the radius into the formula for finding area, area = πr^2. For example, if the diameter is 20 inches, you would divide that in half and get 10 inches. To find the area using the diameter, or the distance from one side of the circle to the other, first divide the diameter in half to find the radius. Therefore, the area of the circle is 113.04 inches squared. Then, you would multiply 36 by π and get 113.04. For example, if the radius of the circle is 6 inches, first you would square 6 and get 36. To find the area using the radius, or the length from the center of the circle to the edge, use the formula area = πr^2, where r is the radius.
You can find the area of a circle using the radius, the diameter, or the circumference.
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