How to determine the middle of the segment using a circul?

In this article, you will learn how to divide this or that segment with the help of such a tool as a compass. After all, there is not always a ruler at hand. Such knowledge will be useful in practice.

Content

Geometry is a subject that is studied in school and has application in practice. Thanks to the knowledge of this item, you can find out the area, the volume of a particular figure, or container, as well as easily divide the segment in half with the help of assistant tools. We will learn further on how to determine the middle of the segment using a circul.

How to determine the middle of the segment using one compass?

It is interesting that it is possible to determine the middle of the segment using a circul without a ruler - this was proved by the Italian Maskeri in the eighteenth century. The construction process is more complicated than with these two tools, but knowledge about this will not interfere. First, we will determine what a segment is. The segment is called a straight line limited by two points. And in order to find the middle of the segment, you will have to build many circles and find many points of their intersection on them until there is the middle of the segment.

If you remember the sequence, constructing circles, then the process of determining the middle is simple. First, they double the segment by constructing two circles with a radius equal to the length of a given segment, photo below:

Circles with a radius in the length of the segment

The next step is to build a circle with the same radius at the top at the intersection of two circles, it will clearly look like this:

From the intersection of the second and third circle, draw another fourth circle of the same radius, this drawing should be obtained:

These circles were built to get a point (the third point, as a continuation of the segment), it is at the intersection of the fourth and second circle. Now leave this point, and rub two circles on top, they will not need them.
Build a circle with a radius twice as much as the previous ones:

Mark two points of intersection on the first circle and large. Through these two points, draw circles with the radius of the segment, and the point of their intersection will be the middle of the segment.

IMPORTANT: Search for the middle of the segment comes down to a few steps. Initially, the segment should be lengthened exactly twice due to a circle of larger diameter, and then near the constructions and find the very point itself, which shares it in half.

How to build the middle of the segment with a circul and ruler?

You can also build the middle of the segment using a circul, ruler. To do this is much easier than in the previous version. You will not need to draw many circles of different diameters, and it is enough to build only two identical ones, and then draw a perpendicular through the intersection with the circle lines. This perpendicular is also called the middle, which means the line, which is carried out at an angle of 90 degrees to the segment.

Then a master class on this topic will be presented in detail and clearly:

Draw the desired segment on the sheet in the cell, so it will be more convenient for you to understand this topic.
Take the compass and draw two circles with a radius more than the middle of the segment or the radius with the length of the segment - there is no particular need to draw too large circles, especially if a segment of a large length.

The figure above shows that the circles form two points of intersection (above and below). Now you will need a ruler. Connect these two points with the middle perpendicular. The crossing point of the line and the segment will be the middle.

So, the middle point of the segment was found, now it will not hurt to prove that it is CD - the middle perpendicular, and it shares the segment in half. It’s easy to do it. After all, two circles that form a line have the same radius, diameter. And in circles, all points on the line are equally removed from its center. So points C and D are also located at the same distances from points A and B. The line that connects points D and C can only be one in the plane. And the intersection point on the segment is at the same distance. All this needed to be clarified.