Perpendicular Bisectors

Let's talk about lines. Let us say we are given a line segment $AB$. We can draw it like this:

Alright. So if we wanted to find some line that is perpendicular to the segment $AB$, we can just find any such line quite easily and draw it so that the angle between the lines is $90^\circ$, like so:

Great! What I have drawn is one such line. And I have marked the point of intersection and labeled it as $M$. Now what if we wanted to make this perpendicular line a bisector of the segment $AB$? All we would have to do is translate the line up or down so that the intersection point, $M$, is the midpoint of the segment.

Great; the line we drew is perpendicular to the segment $AB$ and it is a bisector of segment $AB$. Thus, we call it a perpendicular bisector of segment $AB$.

Perpendicular bisector which comes from a point and is both perpendicular and bisector of line perpendicular means it makes an angle of 90 degrees and bisector means it divides the line into two equal halves. the place of intersection of perpendicular points of a triangle is called a circumcircle . the circumcircle encloses the triangle in a circle

A perpendicular bisector of a line segment is a line dividing the line segment into two equal parts ( bisects it) and at the same time makes an angle of 90 degrees with it. It is infact the locus of all the points that are equidistant from the end points of the line segment.

Example: Perpendicular Bisectors $\\$

A perpendicular bisector of a line segment $l$ is a line that divides $l$ into two equal parts, and it is also perpendicular to $l$.

In fact, the name "perpendicular bisector" tells us exactly what it is.

Perpendicular bisectors are everywhere, for example:

In the image above, the two circles have the same radius. $\overline{CD}$ and $\overline{AB}$ are the perpendicular bisectors of each other. Just by looking at the graph, this is not hard to see. In fact, it can be proven!