How many Planes are there in a Circle?

Geometry is the branch of mathematics that deals with the study of figures, their related dimensions, and measurements. Geometrical figures most commonly can be 2-Dimensional in shape having length and breadth or 3-Dimensional in shape having length, breadth, and height. Geometrical figures can be made up of simple straight lines like square, rectangle in 2D and cube, cuboid in 3-D.  Similarly, they can also be made up of curved lines like circles in 2-D and spheres in 3-D.

Circle

A circle is the most common 2-Dimensional shape. It is formed by curved lines. The circle has a common radius and twice the radius is the diameter of the circle. Below is the given diagram of the circle which is very familiar to everyone. Circle or circular form can be seen in everyday life as well, for instance, the shape of the cookie, plates, etc.

Figure 1: A Circle

So, what happens when a circle is placed on a plane? Or when a Circle is placed on a Plane? Or How many Planes are there in a Circle? Let’s understand the answer to these questions,

How many planes are in a circle?

The plane is a flat surface that is extendable in all directions gets sectioned into parts when a 2- Dimensional Circle is placed on it. The normal plane is a vast space of area that gets divided into three parts when a closed curve circle is placed on it. The three parts or sections are: Inside of a Circle, On the Circle, and Outside of a Circle. These three parts are neither equal in measurement on the basis of the area occupied by them nor on the basis of space occupied by each section.

So, a detailed view of the three divisions of a plane by the circle are as below:

• Inside of a Circle: The points lying within the boundary of the circle fall in the inside of a Circle. This is the interior portion of the circle. Denoted by the shaded region in the figure.

Fig 2: Inside of a Circle 

• On the Circle: The points lying on the boundary of the circle fall in the On a Circle category. This is a portion of the circle i.e the actual circular boundary in the mathematical world. . Denoted by the pointed arrow in the figure.

Fig 3: On the Circle

• Outside of a Circle: The points lying outside the boundary of the circle fall in the outside of a Circle. This is the exterior portion of the circle. Denoted by the shaded region in the figure.

Fig 4: Outside of a Circle

Thus, a circle divides the plane into 3 parts or we can conclude that there are 3 planes formed by a circle.

Conceptual Questions

Question 1: In how many parts does a circle divide a plane into?

Answer:

A circle divides a plane into three parts – Inside of a Circle, On the Circle, and Outside of a Circle. 

Question 2: In the given figure below, which section of the plane does point ‘A’ lie?

Answer:

The given point ‘A’ lies Outside the Circle.

Question 3: Are all the sections of the circle divided plane equal?

Answer:

No, the measurements of the three sections differ in mathematical measurements.

Question 4: In the given figure below, which section of the plane does point ‘X’, ‘Y’, ‘Z’ lie?

Answer:

In the given figure, Point X and Point Y lie Inside of the Circle and Point Z lies Outside of the Circle

Question 5: Given a circle, depict its three sections all in the same figure.

Answer: 

The figure represents the three parts or sections ‘X ‘denotes Inside of a Circle, ‘Y’ denotes On the Circle and ‘Z’ denotes Outside of a Circle. 

Question 6: The boundary of the circle falls under which section of the plane when it gets divided by the circle?

Answer: 

The section: On the Circle represents the boundary of the circle.