How many Axes of Symmetry does a Circle have?

The symmetry axes of a circle they are infinite. These axes are those that divide any geometric shape into two exactly equal halves. And a circle consists of all points whose distance to a fixed point is less than or equal to a certain value"r".

The fixed point mentioned above is called center, and the value"r"is called radius. The radius is the greatest distance there can be between a point on the circle and the center.

On the other hand, any line segment whose ends are at the edge of the circle (circumference) and passing through the center is called diameter. Its measurement is always equal to twice the radius.

Circle and circumference

Do not confuse a circle with a circle. The circumference refers only to the points that are at a distance"r"from the center; that is, only the edge of the circle.

However, when looking for the axes of symmetry it is indifferent if you work with a circle or with a circle.

What is an axis of symmetry?

An axis of symmetry is a line that divides in two equal parts a certain geometric figure. In other words, an axis of symmetry acts like a mirror.

In the previous image it can be seen that the vertical line that passes through the center of the opposite sides of the square is an axis of symmetry of the square.

Shafts of symmetry of a circle

If you observe any circle, regardless of its radius, you can see that not every line that crosses it is an axis of symmetry.

For example, none of the lines drawn in the following image is an axis of symmetry.

An easy way to check if a line is an axis of symmetry or not, is to reflect perpendicularly the geometric figure to the opposite side of the line.

If the reflection does not fit with the original figure, then the line is not an axis of symmetry. The following image illustrates this technique.

But if the following image is considered, it is well known that the line drawn is an axis of symmetry of the circle.

The question is: are there more axes of symmetry? The answer is yes. If you rotate this line 45 ° counterclockwise, the line obtained is also an axis of symmetry of the circle.

The same happens if you rotate 90 °, 30 °, 8 ° and, in general, any number of degrees.

The important thing about these lines is not the inclination they have, but they all go through the center of the circle. Therefore, any line that contains a diameter of the circle is an axis of symmetry.

So, since a circle has an infinite number of diameters, then it has an infinite number of axes of symmetry.

Other geometric figures, such as a triangle, a quadrilateral, a pentagon, a hexagon or any other polygon, have a finite number of axes of symmetry.

The reason why a circle has an infinite number of axes of symmetry is that it has no sides.

References

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