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· **The construction of the perpendicular bisector of a line segment.**

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1. Open a compass more than half the length of the line. Place the point of the compass on one end of the line.

2. Draw an arc above and below the line.

3. Place the point of the compass on the other end of the line. Draw an arc above and below the line to cut the other two arcs. Draw a line connecting the two points where the arcs intersect (meet).

**· The construction of the circumcircle of a triangle.**

1. Draw the triangle.

2. Construct the perpendicular bisector of one side of the triangle.

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how to draw a perpendicular bisector of a tringle?

**: A circumcircle is a circle that passes through all the vertices of any polygon.**

Circumcircle

Circumcircle

Here we draw a circumcircle for a triangle. Let's have a triangle ABC

Now for circumcircle we have two bisect any two sides of our triangle ABC.

Let's First bisect line AB.

For that we follow these steps:

1) First take a compass and open it to more than half length of AB,place the point of the compass at one end of the line i.e. A.

2) Draw an arc on both side of line AB.

3) Now do the first step but place the compass on another end of the line i.e. B. and draw an arc on both side of line AB to cut the first two arcs.

4) Now draw a connecting line for both the arc intersection points:

Now follow all above steps to bisect line AC.

And then these both bisector lines intersect each other at a point 'O' . As:

Now, Place point of the compass at point 'o' and open it to any point of the triangle vertices. let's open it to point A.

and form a circle. As:

This is a circumcircle of triangle ABC.

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