# CONSTRUCTION OF CIRCUMCENTER OF A TRIANGLE

In this section, you will learn how to construct the circumcenter of a triangle.

Key Concept - Circumcenter

The point of concurrency of the perpendicular bisectors of the three sides of a triangle is called the circumcenter and is usually denoted by S.

Before we learn how to construct circumcenter of a triangle, first we have to know how to construct perprendicular bisector.

So, let us learn how to construct a perpendicular bisector.

## Construction of Perpendicular Bisector - Steps

To construct a perpendicular bisector, we must need the following instruments.

1. Ruler

2. Compass

The steps for the construction of a perpendicular bisector of a line segment are :

Step 1 :

Draw the line segment AB.

Step 2 :

With the two end points A and B of the line segment as centers and more than half the length of the line segment as radius draw arcs to intersect on both sides of the line segment at C and D.

Step 3 :

Join C and D to get the perpendicular bisector of the given line segment AB.

In the above figure, CD is the perpendicular bisector of the line segment AB.

This construction clearly shows how to draw the perpendicular bisector of a given line segment with compass and straightedge or ruler.

This bisects the line segment (That is, dividing it into two equal parts) and also perpendicular to it.

Now, let us see how to construct the circumcenter of a triangle.

## Constructing Circumcenter of a Triangle - Steps

Construct the circumcenter of the triangle ABC with AB = 5 cm, A = 70° and B =  70°.

Step 1 :

Draw triangle ABC with the given measurements.

Step 2 :

Construct the perpendicular bisectors of any two sides (AC and BC) as explained above.

The two perpendicular bisectors of the sides AC and BC meet at S which is the circumcentre.

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